Abstract

We in this paper study quantum correlations for two neutral spin-particles coupled with a single-mode optical cavity through the usual magnetic interaction. Two-spin entangled states for both antiparallel and parallel spin-polarizations are generated under the photon coherent-state assumption. Based on the quantum master equation we derive the time-dependent quantum correlation of Clauser-Horne-Shimony-Holt (CHSH) type explicitly in comparison with the well known entanglement-measure concurrence. In the two-spin singlet state, which is recognized as one eigenstate of the system, the CHSH correlation and concurrence remain in their maximum values invariant with time and independent of the average photon-numbers either. The correlation varies periodically with time in the general entangled-states for the low average photon-numbers. When the photon number increases to a certain value the oscillation becomes random and the correlations are suppressed below the Bell bound indicating the decoherence of the entangled states. In the high photon-number limit the coherence revivals periodically such that the CHSH correlation approaches the upper bound value at particular time points associated with the cavity-field period.

© 2017 Optical Society of America

Full Article  |  PDF Article
OSA Recommended Articles
Coherence and entanglement in a two-qubit system

Miguel Orszag and Maritza Hernandez
Adv. Opt. Photon. 2(2) 229-286 (2010)

Nonlinear coupler operating on Werner-like states—entanglement creation, its enhancement, and preservation

A. Kowalewska-Kudłaszyk and W. Leoński
J. Opt. Soc. Am. B 31(6) 1290-1297 (2014)

Spin entanglement, decoherence and Bohm’s EPR paradox

E. G. Cavalcanti, P. D. Drummond, H. A. Bachor, and M. D. Reid
Opt. Express 17(21) 18693-18702 (2009)

References

  • View by:
  • |
  • |
  • |

  1. M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information (Cambridge University Press, 2000).
  2. C. Branciard, N. Brunner, N. Gisin, C. Kurtsiefer, A. Lamas-Linares, A. Ling, and V. Scarani, “Testing quantum correlations versus single-particle properties within Leggett’s model and beyond,” Nat. Phys. 4, 681–685 (2008).
    [Crossref]
  3. S. Gröblacher, T. Paterek, R. Kaltenbaek, Č. Brukner, M. Żukowski, M. Aspelmeyer, and A. Zeilinger, “An experimental test of non-local realism,” Nature 446, 871–875 (2007).
    [Crossref] [PubMed]
  4. T. Paterek, A. Fedrizzi, S. Gröblacher, T. Jennewein, M. Żukowski, M. Aspelmeyer, and A. Zeilinger, “Experimental test of nonlocal realistic theories without the rotational symmetry assumption,” Phys. Rev. Lett. 99, 210406 (2007).
    [Crossref]
  5. S. Pironio, A. Acín, S. Massar, A. Boyer de lai Giroday, D. N. Matsukevich, P. Maunz, S. Olmschenk, D. Hayes, L. Luo, T. A. Manning, and C. Monroe, “Random numbers certified by Bell’s theorem,” Nature 464, 1021–1024 (2010).
    [Crossref] [PubMed]
  6. R. Rabelo, M. Ho, D. Cavalcanti, N. Brunner, and V. Scarani, “Device-independent certification of entangled measurements,” Phys. Rev. Lett. 107, 050502 (2011).
    [Crossref] [PubMed]
  7. G. Jaeger, Entanglement, Information, and the Interpretation of Quantum Mechanics (Springer, 2010).
  8. C. Branciard, A. Ling, N. Gisin, C. Kurtsiefer, A. Lamas-Linares, and V. Scarani, “Experimental falsification of Leggett’s nonlocal variable model,” Phys. Rev. Lett. 99, 210407 (2007).
    [Crossref]
  9. M. D. Eisaman, E. A. Goldschmidt, J. Chen, J. Fan, and A. Migdall, “Experimental test of nonlocal realism using a fiber-based source of polarization-entangled photon pairs,” Phys. Rev. A 77, 032339 (2008).
    [Crossref]
  10. M. Paternostro and H. Jeong, “Testing nonlocal realism with entangled coherent states,” Phys. Rev. A 81, 032115 (2010).
    [Crossref]
  11. C.-W. Lee, M. Paternostro, and H. Jeong, “Faithful test of nonlocal realism with entangled coherent states,” Phys. Rev. A 83, 022102 (2011).
    [Crossref]
  12. M. Pawlowski, T. Paterek, D. Kaszlikowski, V. Scarani, A. Winter, and M. Zukowski, “Information causality as a physical principle,” Nature 461, 1101–1104 (2009).
    [Crossref] [PubMed]
  13. G. Weihs, T. Jennewein, C. Simon, H. Weinfurter, and A. Zeilinger, “Violation of Bell’s inequality under strict Einstein locality conditions,” Phys. Rev. Lett. 81, 5039 (1998).
    [Crossref]
  14. A. Aspect, “Violation of Bell’s inequality under strict Einstein locality conditions,” Nature 398, 189–190 (1999).
    [Crossref]
  15. W. Tittel, J. Brendel, B. Gisin, T. Herzog, H. Zbinden, and N. Gisin, “Experimental demonstration of quantum correlations over more than 10 km,” Phys. Rev. A 57, 3229 (1998).
    [Crossref]
  16. M. A. Rowe, D. Kielpinski, V. Meyer, C. A. Sackett, W. M. Itano, C. Monroe, and D. J. Wineland, “Experimental violation of a Bell’s inequality with efficient detection,” Nature 409, 791–794 (2001).
    [Crossref] [PubMed]
  17. L. F. Wei, Y. X. Liu, and F. Nori, “Testing Bell’s inequality in a constantly coupled Josephson circuit by effective single-qubit operations,” Phys. Rev. B 72, 104516 (2005).
    [Crossref]
  18. P. G. Kwiat, K. Mattle, H. Weinfurter, A. Zeilinger, A. V. Sergienko, and Y. Shih, “New high-intensity source of polarization-entangled photon pairs,” Phy. Rev. Lett. 75, 4337 (1995).
    [Crossref]
  19. H. Sakai, T. Saito, T. Ikeda, K. Itoh, T. Kawabata, H. Kuboki, Y. Maeda, N. Matsui, C. Rangacharyulu, M. Sasano, Y. Satou, K. Sekiguchi, K. Suda, A. Tamii, T. Uesaka, and K. Yako, “Spin correlations of strongly interacting massive fermion pairs as a test of Bell’s inequality,” Phys. Rev. Lett. 97, 150405 (2006).
    [Crossref]
  20. A. C. Dada, J. Leach, G. S. Buller, M. J. Padgett, and E. Andersson, “Experimental high-dimensional two-photon entanglement and violations of generalized Bell inequalities,” Nat. Phys. 7, 677–680 (2011).
    [Crossref]
  21. J. Barrett, D. Collins, L. Hardy, A. Kent, and S. Popescu, “Quantum nonlocality, Bell inequalities, and the memory loophole,” Phys. Rev. A 66, 042111 (2002).
    [Crossref]
  22. Y. Zhang, S. Glancy, and E. Knill, “Asymptotically optimal data analysis for rejecting local realism,” Phy. Rev. A 84, 062118 (2011).
    [Crossref]
  23. P. Pandya, A. Misra, and I. Chakrabarty, “Complementarity between tripartite quantum correlation and bipartite Bell-inequality violation in three-qubit states,” Phys. Rev. A 94, 052126 (2016).
    [Crossref]
  24. A. A. Semenov and W. Vogel, “Entanglement transfer through the turbulent atmosphere,” Phys. Rev. A 81, 023835 (2010).
    [Crossref]
  25. M. O. Gumberidze, A. A. Semenov, D. Vasylyev, and W. Vogel, “Bell nonlocality in the turbulent atmosphere,” Phys. Rev. A 94, 053801 (2016).
    [Crossref]
  26. L. Mazzola, B. Bellomo, R. L. Franco, and G. Compagno, “Bell nonlocality in the turbulent atmosphere,” Phys. Rev. A 81, 052116 (2010).
    [Crossref]
  27. A. G. Kofman and A. N. Korotkov, “Bell-inequality violation versus entanglement in the presence of local decoherence,” Phys. Rev. A 77, 052329 (2008).
    [Crossref]
  28. J. Q. Li and J. Q. Liang, “Disentanglement and Bell nonlocality in a classical dephasing environment,” Phys. Lett. A 374, 1975–1979 (2010).
    [Crossref]
  29. F. Altintas and R. J. Eryigit, “Dynamics of entanglement and Bell non-locality for two stochastic qubits with dipole–dipole interaction,” J. Phys. A: Math. Theor. 43, 415306 (2010).
    [Crossref]
  30. Ł. Derkacz and L. Jakobczyk, “Clauser-Horne-Shimony-Holt violation and the entropy-concurrence plane,” Phys. Rev. A 72, 042321 (2005).
    [Crossref]
  31. R. F. Werner, “Quantum states with Einstein-Podolsky-Rosen correlations admitting a hidden-variable model,” Phys. Rev. A 40, 4277 (1989).
    [Crossref]
  32. J. F. Clauser, M. A. Horne, A. Shimony, and R. A. Holt, “Proposed experiment to test local hidden-variable theories,” Phys. Rev. Lett. 23, 880 (1969).
    [Crossref]
  33. P. Bierhorst, “A robust mathematical model for a loophole-free Clauser–Horne experiment,” J. Phys. A 48, 195302 (2015).
    [Crossref]
  34. A. J. Leggett, “Nonlocal hidden-variable theories and quantum mechanics: An incompatibility theorem,” Found. Phys. 33, 1469–1493 (2003).
    [Crossref]
  35. B. Hensen, H. Bernien, A. E. Dréau, A. Reiserer, N. Kalb, M. S. Blok, J. Ruitenberg, R. F. L. Vermeulen, R. N. Schouten, C. Abellán, W. Amaya, V. Pruneri, M. W. Mitchell, M. Markham, D. J. Twitchen, D. Elkouss, S. Wehner, T. H. Taminiau, and R. Hanson, “Loophole-free Bell inequality violation using electron spins separated by 1.3 kilometres,” Nature 526, 682–686 (2015).
    [Crossref] [PubMed]
  36. M. T. Quintino, T. Vértesi, and N. Brunner, “Joint measurability, einstein-podolsky-rosen steering, and bell nonlocality,” Phys. Rev. Lett. 113, 160402 (2014).
    [Crossref] [PubMed]
  37. M. Żukowski, A. Dutta, and Z. Yin, “Geometric Bell-like inequalities for steering,” Phys. Rev. A 91, 032107 (2015).
    [Crossref]
  38. A. Roy, S. S. Bhattacharya, A. Mukherjee, and M. Banik, “Optimal quantum violation of Clauser-Horne-Shimony-Holt like steering inequality,” J. Phys. A 48, 415302 (2015).
    [Crossref]
  39. X. L. Zhen, Q. Yang, M. Yang, and Z. L. Cao, “Bell-Nonlocality Dynamics of Three Remote Atoms in Tavis— Cummings and Jaynes—Cummings Models,” Commun. Theor. Phys. 62, 795–800 (2014).
    [Crossref]
  40. R. X. Chen, C. Hu, and L. Miao, “Dynamics of Bell-nonlocality of two-mode squeezed vacuum fields interacting with atoms,” Opt. Commun. 284, 2955–2959 (2011).
    [Crossref]
  41. S. B. Li and J. B. Xu, “Entanglement, Bell violation, and phase decoherence of two atoms inside an optical cavity,” Phys. Rev. A 72, 022332 (2005).
    [Crossref]
  42. J.-B. Xu and S.-B. Li, “Control of the entanglement of two atoms in an optical cavity via white noise,” New J. Phys. 7, 72 (2005).
    [Crossref]
  43. T. M. Stace, G. J. Milburn, and C. H. W. Barnes, “Entangled two-photon source using biexciton emission of an asymmetric quantum dot in a cavity,” Phys. Rev. B 67, 085317 (2003).
    [Crossref]
  44. B. Wang, Z. Y. Xu, Z. Q. Chen, and M. Feng, “Non-Markovian effect on the quantum discord,” Phys. Rev. A 81, 014101 (2010).
    [Crossref]
  45. R. C. Ge, M. Gong, C. F. Li, J. S. Xu, and G. C. Guo, “Quantum correlation and classical correlation dynamics in the spin-boson model,” Phys. Rev. A 81, 064103 (2010).
    [Crossref]
  46. F. Francica, F. Plastina, and S. Maniscalco, “Quantum Zeno and anti-Zeno effects on quantum and classical correlations,” Phys. Rev. A 82, 052118 (2010).
    [Crossref]
  47. G. Waldherr, P. Neumann, S. F. Huelga, F. Jelezko, and J. Wrachtrup, “Violation of a temporal Bell inequality for single spins in a diamond defect center,” Phys. Rev. Lett. 107, 090401 (2011).
    [Crossref] [PubMed]
  48. B. Hensen, N. Kalb, M. S. Blok, A. E. Dréau, A. Reiserer, R. F. L. Vermeulen, R. N. Schouten, M. Markham, D. J. Twitchen, K. Goodenough, D. Elkouss, S. Wehner, T. H. Taminiau, and R. Hansona, “Loophole-free Bell test using electron spins in diamond: second experiment and additional analysis,” Sci. Rep. 6, 30289 (2016).
    [Crossref] [PubMed]
  49. X.-D. Chen, L.-M. Zhou, C.-L. Zou, C.-C. Li, Y. Dong, F.-W. Sun, and G.-C. Guo, “Spin depolarization effect induced by charge state conversion of nitrogen vacancy center in diamond,” Phys. Rev. B 92, 104301 (2015).
    [Crossref]
  50. N. Zhao, J.-L. Hu, S.-W. Ho, J. T. K. Wan, and R. B. Liu, “Atomic-scale magnetometry of distant nuclear spin clusters via nitrogen-vacancy spin in diamond,” Nat. Nanotech. 6, 242–246 (2011).
    [Crossref]
  51. N. Zhao and Z. Yin, “Room-temperature ultrasensitive mass spectrometer via dynamical decoupling,” Phys. Rev. A 90, 042118 (2014).
    [Crossref]
  52. Z. Yin, T. Li, X. Zhang, and L. M. Duan, “Large quantum superpositions of a levitated nanodiamond through spin-optomechanical coupling,” Phys. Rev. A 88, 033614 (2013).
    [Crossref]
  53. M. Scala, M. S. Kim, G. W. Morley, P. F. Barker, and S. Bose, “Matter-wave interferometry of a levitated thermal nano-oscillator induced and probed by a spin,” Phys. Rev. Lett. 111, 180403 (2013).
    [Crossref] [PubMed]
  54. S. Kolkowitz, A. C. B. Jayich, Q. P. Unterreithmeier, S. D. Bennett, P. Rabl, J. G. E. Harris, and M. D. Lukin, “Coherent sensing of a mechanical resonator with a single-spin qubit,” Science 335, 1603–1606 (2012).
    [Crossref] [PubMed]
  55. F. Altintas and R. Eryigit, “Quantum correlations in non-Markovian environments,” Phys. Lett. A 374, 4283 (2010).
    [Crossref]
  56. Z. Sun, X. M. Lu, and L. J. Song, “Quantum discord induced by a spin chain with quantum phase transition,” J. Phys. B: At. Mol. Opt. Phys. 43, 215504 (2010).
    [Crossref]
  57. X. M. Lu, Z. Xi, Z. Sun, and X. Wang, “Geometric measure of quantum discord under decoherence,” Quantum Inf. Comput. 10, 994–1003 (2010).
  58. T. Werlang, S. Souza, F. F. Fanchini, and C. J. V. Boas, “Robustness of quantum discord to sudden death,” Phys. Rev. A 80, 024103 (2009).
    [Crossref]
  59. X. Hao, C. L. Ma, and J. Sha, “Decoherence of quantum discord in an asymmetric-anisotropy spin system,” J. Phys. A: Math. Theor. 43, 425302 (2010).
    [Crossref]
  60. J. B. Yuan, L. M. Kuang, and J. Q. Liao, “Amplification of quantum discord between two uncoupled qubits in a common environment by phase decoherence,” J. Phys. B: At. Mol. Opt. Phys. 43, 165503 (2010).
    [Crossref]
  61. E. Polozova and F. W. Strauch, “Higher-dimensional Bell inequalities with noisy qudits,” Phys. Rev. A 93, 032130 (2016).
    [Crossref]
  62. M. Ansmann, H. Wang, R. C. Bialczak, M. Hofheinz, E. Lucero, M. Neeley, A. D. O’Connell, D. Sank, M. Weides, J. Wenner, A. N. Cleland, and J. M. Martinis, “Violation of Bell’s inequality in Josephson phase qubits,” Nature 461, 504–506 (2009).
    [Crossref] [PubMed]
  63. Z. Song, J.-Q. Liang, and L.-F. Wei, “Spin-Parity Effect in Violation of Bell’s Inequalities,” Mod. Phys. Lett. B 28, 1450004 (2014).
    [Crossref]
  64. X. Q. Zhao, N. Liu, and J.-Q. Liang, “Nonlinear atom-photon-interaction-induced population inversion and inverted quantum phase transition of Bose-Einstein condensate in an optical cavity,” Phys. Rev. A 90, 023622 (2014).
    [Crossref]
  65. Z. M. Wang, J. L. Lian, J.-Q. Liang, W-M Liu, and Y. M. Yu, “Collapse of the superradiant phase and multiple quantum phase transitions for Bose-Einstein condensates in an optomechanical cavity,” Phys. Rev. A 93, 033630 (2016).
    [Crossref]
  66. M. H. Wang, L. F. Wei, and J.-Q. Liang, “Does the Berry phase in a quantum optical system originate from the rotating wave approximation,” Phys. Lett. A 379, 1087–1090 (2015).
    [Crossref]
  67. H. F. Zhang, J. H. Wang, Z. G. Song, J.-Q. Liang, and L.-F. Wei, “Spin-parity effect in violation of bell’s inequalities for entangled states of parallel polarization,” Mod. Phys. Lett. B 31, 1750032 (2017).
    [Crossref]
  68. R. Horodecki, P. Horodecki, and M. Horodecki, “Violating Bell inequality by mixed spin-12 states: necessary and sufficient condition,” Phys. Lett. A 200, 340–344 (1995).
    [Crossref]
  69. R. Horodecki, “Two-spin-12 mixtures and Bell’s inequalities,” Phys. Lett. A 210, 223–226 (1996).
    [Crossref]
  70. M. S. Kim, J. Lee, D. Ahn, and P. L. Knight, “Entanglement induced by a single-mode heat environment,” Phys. Rev. A 65, 040101 (2002).
    [Crossref]
  71. W. K. Wootters, “Entanglement of formation of an arbitrary state of two qubits,” Phys. Rev. Lett. 80, 2245 (1998).
    [Crossref]
  72. N. Gisin, “Bell’s inequality holds for all non-product states,” Phys. Lett. A 154, 201–202 (1991).
    [Crossref]

2017 (1)

H. F. Zhang, J. H. Wang, Z. G. Song, J.-Q. Liang, and L.-F. Wei, “Spin-parity effect in violation of bell’s inequalities for entangled states of parallel polarization,” Mod. Phys. Lett. B 31, 1750032 (2017).
[Crossref]

2016 (5)

Z. M. Wang, J. L. Lian, J.-Q. Liang, W-M Liu, and Y. M. Yu, “Collapse of the superradiant phase and multiple quantum phase transitions for Bose-Einstein condensates in an optomechanical cavity,” Phys. Rev. A 93, 033630 (2016).
[Crossref]

E. Polozova and F. W. Strauch, “Higher-dimensional Bell inequalities with noisy qudits,” Phys. Rev. A 93, 032130 (2016).
[Crossref]

B. Hensen, N. Kalb, M. S. Blok, A. E. Dréau, A. Reiserer, R. F. L. Vermeulen, R. N. Schouten, M. Markham, D. J. Twitchen, K. Goodenough, D. Elkouss, S. Wehner, T. H. Taminiau, and R. Hansona, “Loophole-free Bell test using electron spins in diamond: second experiment and additional analysis,” Sci. Rep. 6, 30289 (2016).
[Crossref] [PubMed]

P. Pandya, A. Misra, and I. Chakrabarty, “Complementarity between tripartite quantum correlation and bipartite Bell-inequality violation in three-qubit states,” Phys. Rev. A 94, 052126 (2016).
[Crossref]

M. O. Gumberidze, A. A. Semenov, D. Vasylyev, and W. Vogel, “Bell nonlocality in the turbulent atmosphere,” Phys. Rev. A 94, 053801 (2016).
[Crossref]

2015 (6)

P. Bierhorst, “A robust mathematical model for a loophole-free Clauser–Horne experiment,” J. Phys. A 48, 195302 (2015).
[Crossref]

M. Żukowski, A. Dutta, and Z. Yin, “Geometric Bell-like inequalities for steering,” Phys. Rev. A 91, 032107 (2015).
[Crossref]

A. Roy, S. S. Bhattacharya, A. Mukherjee, and M. Banik, “Optimal quantum violation of Clauser-Horne-Shimony-Holt like steering inequality,” J. Phys. A 48, 415302 (2015).
[Crossref]

X.-D. Chen, L.-M. Zhou, C.-L. Zou, C.-C. Li, Y. Dong, F.-W. Sun, and G.-C. Guo, “Spin depolarization effect induced by charge state conversion of nitrogen vacancy center in diamond,” Phys. Rev. B 92, 104301 (2015).
[Crossref]

B. Hensen, H. Bernien, A. E. Dréau, A. Reiserer, N. Kalb, M. S. Blok, J. Ruitenberg, R. F. L. Vermeulen, R. N. Schouten, C. Abellán, W. Amaya, V. Pruneri, M. W. Mitchell, M. Markham, D. J. Twitchen, D. Elkouss, S. Wehner, T. H. Taminiau, and R. Hanson, “Loophole-free Bell inequality violation using electron spins separated by 1.3 kilometres,” Nature 526, 682–686 (2015).
[Crossref] [PubMed]

M. H. Wang, L. F. Wei, and J.-Q. Liang, “Does the Berry phase in a quantum optical system originate from the rotating wave approximation,” Phys. Lett. A 379, 1087–1090 (2015).
[Crossref]

2014 (5)

Z. Song, J.-Q. Liang, and L.-F. Wei, “Spin-Parity Effect in Violation of Bell’s Inequalities,” Mod. Phys. Lett. B 28, 1450004 (2014).
[Crossref]

X. Q. Zhao, N. Liu, and J.-Q. Liang, “Nonlinear atom-photon-interaction-induced population inversion and inverted quantum phase transition of Bose-Einstein condensate in an optical cavity,” Phys. Rev. A 90, 023622 (2014).
[Crossref]

M. T. Quintino, T. Vértesi, and N. Brunner, “Joint measurability, einstein-podolsky-rosen steering, and bell nonlocality,” Phys. Rev. Lett. 113, 160402 (2014).
[Crossref] [PubMed]

N. Zhao and Z. Yin, “Room-temperature ultrasensitive mass spectrometer via dynamical decoupling,” Phys. Rev. A 90, 042118 (2014).
[Crossref]

X. L. Zhen, Q. Yang, M. Yang, and Z. L. Cao, “Bell-Nonlocality Dynamics of Three Remote Atoms in Tavis— Cummings and Jaynes—Cummings Models,” Commun. Theor. Phys. 62, 795–800 (2014).
[Crossref]

2013 (2)

Z. Yin, T. Li, X. Zhang, and L. M. Duan, “Large quantum superpositions of a levitated nanodiamond through spin-optomechanical coupling,” Phys. Rev. A 88, 033614 (2013).
[Crossref]

M. Scala, M. S. Kim, G. W. Morley, P. F. Barker, and S. Bose, “Matter-wave interferometry of a levitated thermal nano-oscillator induced and probed by a spin,” Phys. Rev. Lett. 111, 180403 (2013).
[Crossref] [PubMed]

2012 (1)

S. Kolkowitz, A. C. B. Jayich, Q. P. Unterreithmeier, S. D. Bennett, P. Rabl, J. G. E. Harris, and M. D. Lukin, “Coherent sensing of a mechanical resonator with a single-spin qubit,” Science 335, 1603–1606 (2012).
[Crossref] [PubMed]

2011 (7)

N. Zhao, J.-L. Hu, S.-W. Ho, J. T. K. Wan, and R. B. Liu, “Atomic-scale magnetometry of distant nuclear spin clusters via nitrogen-vacancy spin in diamond,” Nat. Nanotech. 6, 242–246 (2011).
[Crossref]

G. Waldherr, P. Neumann, S. F. Huelga, F. Jelezko, and J. Wrachtrup, “Violation of a temporal Bell inequality for single spins in a diamond defect center,” Phys. Rev. Lett. 107, 090401 (2011).
[Crossref] [PubMed]

R. X. Chen, C. Hu, and L. Miao, “Dynamics of Bell-nonlocality of two-mode squeezed vacuum fields interacting with atoms,” Opt. Commun. 284, 2955–2959 (2011).
[Crossref]

Y. Zhang, S. Glancy, and E. Knill, “Asymptotically optimal data analysis for rejecting local realism,” Phy. Rev. A 84, 062118 (2011).
[Crossref]

R. Rabelo, M. Ho, D. Cavalcanti, N. Brunner, and V. Scarani, “Device-independent certification of entangled measurements,” Phys. Rev. Lett. 107, 050502 (2011).
[Crossref] [PubMed]

C.-W. Lee, M. Paternostro, and H. Jeong, “Faithful test of nonlocal realism with entangled coherent states,” Phys. Rev. A 83, 022102 (2011).
[Crossref]

A. C. Dada, J. Leach, G. S. Buller, M. J. Padgett, and E. Andersson, “Experimental high-dimensional two-photon entanglement and violations of generalized Bell inequalities,” Nat. Phys. 7, 677–680 (2011).
[Crossref]

2010 (14)

M. Paternostro and H. Jeong, “Testing nonlocal realism with entangled coherent states,” Phys. Rev. A 81, 032115 (2010).
[Crossref]

S. Pironio, A. Acín, S. Massar, A. Boyer de lai Giroday, D. N. Matsukevich, P. Maunz, S. Olmschenk, D. Hayes, L. Luo, T. A. Manning, and C. Monroe, “Random numbers certified by Bell’s theorem,” Nature 464, 1021–1024 (2010).
[Crossref] [PubMed]

A. A. Semenov and W. Vogel, “Entanglement transfer through the turbulent atmosphere,” Phys. Rev. A 81, 023835 (2010).
[Crossref]

J. Q. Li and J. Q. Liang, “Disentanglement and Bell nonlocality in a classical dephasing environment,” Phys. Lett. A 374, 1975–1979 (2010).
[Crossref]

F. Altintas and R. J. Eryigit, “Dynamics of entanglement and Bell non-locality for two stochastic qubits with dipole–dipole interaction,” J. Phys. A: Math. Theor. 43, 415306 (2010).
[Crossref]

L. Mazzola, B. Bellomo, R. L. Franco, and G. Compagno, “Bell nonlocality in the turbulent atmosphere,” Phys. Rev. A 81, 052116 (2010).
[Crossref]

X. Hao, C. L. Ma, and J. Sha, “Decoherence of quantum discord in an asymmetric-anisotropy spin system,” J. Phys. A: Math. Theor. 43, 425302 (2010).
[Crossref]

J. B. Yuan, L. M. Kuang, and J. Q. Liao, “Amplification of quantum discord between two uncoupled qubits in a common environment by phase decoherence,” J. Phys. B: At. Mol. Opt. Phys. 43, 165503 (2010).
[Crossref]

B. Wang, Z. Y. Xu, Z. Q. Chen, and M. Feng, “Non-Markovian effect on the quantum discord,” Phys. Rev. A 81, 014101 (2010).
[Crossref]

R. C. Ge, M. Gong, C. F. Li, J. S. Xu, and G. C. Guo, “Quantum correlation and classical correlation dynamics in the spin-boson model,” Phys. Rev. A 81, 064103 (2010).
[Crossref]

F. Francica, F. Plastina, and S. Maniscalco, “Quantum Zeno and anti-Zeno effects on quantum and classical correlations,” Phys. Rev. A 82, 052118 (2010).
[Crossref]

F. Altintas and R. Eryigit, “Quantum correlations in non-Markovian environments,” Phys. Lett. A 374, 4283 (2010).
[Crossref]

Z. Sun, X. M. Lu, and L. J. Song, “Quantum discord induced by a spin chain with quantum phase transition,” J. Phys. B: At. Mol. Opt. Phys. 43, 215504 (2010).
[Crossref]

X. M. Lu, Z. Xi, Z. Sun, and X. Wang, “Geometric measure of quantum discord under decoherence,” Quantum Inf. Comput. 10, 994–1003 (2010).

2009 (3)

T. Werlang, S. Souza, F. F. Fanchini, and C. J. V. Boas, “Robustness of quantum discord to sudden death,” Phys. Rev. A 80, 024103 (2009).
[Crossref]

M. Ansmann, H. Wang, R. C. Bialczak, M. Hofheinz, E. Lucero, M. Neeley, A. D. O’Connell, D. Sank, M. Weides, J. Wenner, A. N. Cleland, and J. M. Martinis, “Violation of Bell’s inequality in Josephson phase qubits,” Nature 461, 504–506 (2009).
[Crossref] [PubMed]

M. Pawlowski, T. Paterek, D. Kaszlikowski, V. Scarani, A. Winter, and M. Zukowski, “Information causality as a physical principle,” Nature 461, 1101–1104 (2009).
[Crossref] [PubMed]

2008 (3)

M. D. Eisaman, E. A. Goldschmidt, J. Chen, J. Fan, and A. Migdall, “Experimental test of nonlocal realism using a fiber-based source of polarization-entangled photon pairs,” Phys. Rev. A 77, 032339 (2008).
[Crossref]

C. Branciard, N. Brunner, N. Gisin, C. Kurtsiefer, A. Lamas-Linares, A. Ling, and V. Scarani, “Testing quantum correlations versus single-particle properties within Leggett’s model and beyond,” Nat. Phys. 4, 681–685 (2008).
[Crossref]

A. G. Kofman and A. N. Korotkov, “Bell-inequality violation versus entanglement in the presence of local decoherence,” Phys. Rev. A 77, 052329 (2008).
[Crossref]

2007 (3)

S. Gröblacher, T. Paterek, R. Kaltenbaek, Č. Brukner, M. Żukowski, M. Aspelmeyer, and A. Zeilinger, “An experimental test of non-local realism,” Nature 446, 871–875 (2007).
[Crossref] [PubMed]

T. Paterek, A. Fedrizzi, S. Gröblacher, T. Jennewein, M. Żukowski, M. Aspelmeyer, and A. Zeilinger, “Experimental test of nonlocal realistic theories without the rotational symmetry assumption,” Phys. Rev. Lett. 99, 210406 (2007).
[Crossref]

C. Branciard, A. Ling, N. Gisin, C. Kurtsiefer, A. Lamas-Linares, and V. Scarani, “Experimental falsification of Leggett’s nonlocal variable model,” Phys. Rev. Lett. 99, 210407 (2007).
[Crossref]

2006 (1)

H. Sakai, T. Saito, T. Ikeda, K. Itoh, T. Kawabata, H. Kuboki, Y. Maeda, N. Matsui, C. Rangacharyulu, M. Sasano, Y. Satou, K. Sekiguchi, K. Suda, A. Tamii, T. Uesaka, and K. Yako, “Spin correlations of strongly interacting massive fermion pairs as a test of Bell’s inequality,” Phys. Rev. Lett. 97, 150405 (2006).
[Crossref]

2005 (4)

Ł. Derkacz and L. Jakobczyk, “Clauser-Horne-Shimony-Holt violation and the entropy-concurrence plane,” Phys. Rev. A 72, 042321 (2005).
[Crossref]

S. B. Li and J. B. Xu, “Entanglement, Bell violation, and phase decoherence of two atoms inside an optical cavity,” Phys. Rev. A 72, 022332 (2005).
[Crossref]

J.-B. Xu and S.-B. Li, “Control of the entanglement of two atoms in an optical cavity via white noise,” New J. Phys. 7, 72 (2005).
[Crossref]

L. F. Wei, Y. X. Liu, and F. Nori, “Testing Bell’s inequality in a constantly coupled Josephson circuit by effective single-qubit operations,” Phys. Rev. B 72, 104516 (2005).
[Crossref]

2003 (2)

T. M. Stace, G. J. Milburn, and C. H. W. Barnes, “Entangled two-photon source using biexciton emission of an asymmetric quantum dot in a cavity,” Phys. Rev. B 67, 085317 (2003).
[Crossref]

A. J. Leggett, “Nonlocal hidden-variable theories and quantum mechanics: An incompatibility theorem,” Found. Phys. 33, 1469–1493 (2003).
[Crossref]

2002 (2)

J. Barrett, D. Collins, L. Hardy, A. Kent, and S. Popescu, “Quantum nonlocality, Bell inequalities, and the memory loophole,” Phys. Rev. A 66, 042111 (2002).
[Crossref]

M. S. Kim, J. Lee, D. Ahn, and P. L. Knight, “Entanglement induced by a single-mode heat environment,” Phys. Rev. A 65, 040101 (2002).
[Crossref]

2001 (1)

M. A. Rowe, D. Kielpinski, V. Meyer, C. A. Sackett, W. M. Itano, C. Monroe, and D. J. Wineland, “Experimental violation of a Bell’s inequality with efficient detection,” Nature 409, 791–794 (2001).
[Crossref] [PubMed]

1999 (1)

A. Aspect, “Violation of Bell’s inequality under strict Einstein locality conditions,” Nature 398, 189–190 (1999).
[Crossref]

1998 (3)

W. Tittel, J. Brendel, B. Gisin, T. Herzog, H. Zbinden, and N. Gisin, “Experimental demonstration of quantum correlations over more than 10 km,” Phys. Rev. A 57, 3229 (1998).
[Crossref]

G. Weihs, T. Jennewein, C. Simon, H. Weinfurter, and A. Zeilinger, “Violation of Bell’s inequality under strict Einstein locality conditions,” Phys. Rev. Lett. 81, 5039 (1998).
[Crossref]

W. K. Wootters, “Entanglement of formation of an arbitrary state of two qubits,” Phys. Rev. Lett. 80, 2245 (1998).
[Crossref]

1996 (1)

R. Horodecki, “Two-spin-12 mixtures and Bell’s inequalities,” Phys. Lett. A 210, 223–226 (1996).
[Crossref]

1995 (2)

R. Horodecki, P. Horodecki, and M. Horodecki, “Violating Bell inequality by mixed spin-12 states: necessary and sufficient condition,” Phys. Lett. A 200, 340–344 (1995).
[Crossref]

P. G. Kwiat, K. Mattle, H. Weinfurter, A. Zeilinger, A. V. Sergienko, and Y. Shih, “New high-intensity source of polarization-entangled photon pairs,” Phy. Rev. Lett. 75, 4337 (1995).
[Crossref]

1991 (1)

N. Gisin, “Bell’s inequality holds for all non-product states,” Phys. Lett. A 154, 201–202 (1991).
[Crossref]

1989 (1)

R. F. Werner, “Quantum states with Einstein-Podolsky-Rosen correlations admitting a hidden-variable model,” Phys. Rev. A 40, 4277 (1989).
[Crossref]

1969 (1)

J. F. Clauser, M. A. Horne, A. Shimony, and R. A. Holt, “Proposed experiment to test local hidden-variable theories,” Phys. Rev. Lett. 23, 880 (1969).
[Crossref]

Abellán, C.

B. Hensen, H. Bernien, A. E. Dréau, A. Reiserer, N. Kalb, M. S. Blok, J. Ruitenberg, R. F. L. Vermeulen, R. N. Schouten, C. Abellán, W. Amaya, V. Pruneri, M. W. Mitchell, M. Markham, D. J. Twitchen, D. Elkouss, S. Wehner, T. H. Taminiau, and R. Hanson, “Loophole-free Bell inequality violation using electron spins separated by 1.3 kilometres,” Nature 526, 682–686 (2015).
[Crossref] [PubMed]

Acín, A.

S. Pironio, A. Acín, S. Massar, A. Boyer de lai Giroday, D. N. Matsukevich, P. Maunz, S. Olmschenk, D. Hayes, L. Luo, T. A. Manning, and C. Monroe, “Random numbers certified by Bell’s theorem,” Nature 464, 1021–1024 (2010).
[Crossref] [PubMed]

Ahn, D.

M. S. Kim, J. Lee, D. Ahn, and P. L. Knight, “Entanglement induced by a single-mode heat environment,” Phys. Rev. A 65, 040101 (2002).
[Crossref]

Altintas, F.

F. Altintas and R. J. Eryigit, “Dynamics of entanglement and Bell non-locality for two stochastic qubits with dipole–dipole interaction,” J. Phys. A: Math. Theor. 43, 415306 (2010).
[Crossref]

F. Altintas and R. Eryigit, “Quantum correlations in non-Markovian environments,” Phys. Lett. A 374, 4283 (2010).
[Crossref]

Amaya, W.

B. Hensen, H. Bernien, A. E. Dréau, A. Reiserer, N. Kalb, M. S. Blok, J. Ruitenberg, R. F. L. Vermeulen, R. N. Schouten, C. Abellán, W. Amaya, V. Pruneri, M. W. Mitchell, M. Markham, D. J. Twitchen, D. Elkouss, S. Wehner, T. H. Taminiau, and R. Hanson, “Loophole-free Bell inequality violation using electron spins separated by 1.3 kilometres,” Nature 526, 682–686 (2015).
[Crossref] [PubMed]

Andersson, E.

A. C. Dada, J. Leach, G. S. Buller, M. J. Padgett, and E. Andersson, “Experimental high-dimensional two-photon entanglement and violations of generalized Bell inequalities,” Nat. Phys. 7, 677–680 (2011).
[Crossref]

Ansmann, M.

M. Ansmann, H. Wang, R. C. Bialczak, M. Hofheinz, E. Lucero, M. Neeley, A. D. O’Connell, D. Sank, M. Weides, J. Wenner, A. N. Cleland, and J. M. Martinis, “Violation of Bell’s inequality in Josephson phase qubits,” Nature 461, 504–506 (2009).
[Crossref] [PubMed]

Aspect, A.

A. Aspect, “Violation of Bell’s inequality under strict Einstein locality conditions,” Nature 398, 189–190 (1999).
[Crossref]

Aspelmeyer, M.

T. Paterek, A. Fedrizzi, S. Gröblacher, T. Jennewein, M. Żukowski, M. Aspelmeyer, and A. Zeilinger, “Experimental test of nonlocal realistic theories without the rotational symmetry assumption,” Phys. Rev. Lett. 99, 210406 (2007).
[Crossref]

S. Gröblacher, T. Paterek, R. Kaltenbaek, Č. Brukner, M. Żukowski, M. Aspelmeyer, and A. Zeilinger, “An experimental test of non-local realism,” Nature 446, 871–875 (2007).
[Crossref] [PubMed]

Banik, M.

A. Roy, S. S. Bhattacharya, A. Mukherjee, and M. Banik, “Optimal quantum violation of Clauser-Horne-Shimony-Holt like steering inequality,” J. Phys. A 48, 415302 (2015).
[Crossref]

Barker, P. F.

M. Scala, M. S. Kim, G. W. Morley, P. F. Barker, and S. Bose, “Matter-wave interferometry of a levitated thermal nano-oscillator induced and probed by a spin,” Phys. Rev. Lett. 111, 180403 (2013).
[Crossref] [PubMed]

Barnes, C. H. W.

T. M. Stace, G. J. Milburn, and C. H. W. Barnes, “Entangled two-photon source using biexciton emission of an asymmetric quantum dot in a cavity,” Phys. Rev. B 67, 085317 (2003).
[Crossref]

Barrett, J.

J. Barrett, D. Collins, L. Hardy, A. Kent, and S. Popescu, “Quantum nonlocality, Bell inequalities, and the memory loophole,” Phys. Rev. A 66, 042111 (2002).
[Crossref]

Bellomo, B.

L. Mazzola, B. Bellomo, R. L. Franco, and G. Compagno, “Bell nonlocality in the turbulent atmosphere,” Phys. Rev. A 81, 052116 (2010).
[Crossref]

Bennett, S. D.

S. Kolkowitz, A. C. B. Jayich, Q. P. Unterreithmeier, S. D. Bennett, P. Rabl, J. G. E. Harris, and M. D. Lukin, “Coherent sensing of a mechanical resonator with a single-spin qubit,” Science 335, 1603–1606 (2012).
[Crossref] [PubMed]

Bernien, H.

B. Hensen, H. Bernien, A. E. Dréau, A. Reiserer, N. Kalb, M. S. Blok, J. Ruitenberg, R. F. L. Vermeulen, R. N. Schouten, C. Abellán, W. Amaya, V. Pruneri, M. W. Mitchell, M. Markham, D. J. Twitchen, D. Elkouss, S. Wehner, T. H. Taminiau, and R. Hanson, “Loophole-free Bell inequality violation using electron spins separated by 1.3 kilometres,” Nature 526, 682–686 (2015).
[Crossref] [PubMed]

Bhattacharya, S. S.

A. Roy, S. S. Bhattacharya, A. Mukherjee, and M. Banik, “Optimal quantum violation of Clauser-Horne-Shimony-Holt like steering inequality,” J. Phys. A 48, 415302 (2015).
[Crossref]

Bialczak, R. C.

M. Ansmann, H. Wang, R. C. Bialczak, M. Hofheinz, E. Lucero, M. Neeley, A. D. O’Connell, D. Sank, M. Weides, J. Wenner, A. N. Cleland, and J. M. Martinis, “Violation of Bell’s inequality in Josephson phase qubits,” Nature 461, 504–506 (2009).
[Crossref] [PubMed]

Bierhorst, P.

P. Bierhorst, “A robust mathematical model for a loophole-free Clauser–Horne experiment,” J. Phys. A 48, 195302 (2015).
[Crossref]

Blok, M. S.

B. Hensen, N. Kalb, M. S. Blok, A. E. Dréau, A. Reiserer, R. F. L. Vermeulen, R. N. Schouten, M. Markham, D. J. Twitchen, K. Goodenough, D. Elkouss, S. Wehner, T. H. Taminiau, and R. Hansona, “Loophole-free Bell test using electron spins in diamond: second experiment and additional analysis,” Sci. Rep. 6, 30289 (2016).
[Crossref] [PubMed]

B. Hensen, H. Bernien, A. E. Dréau, A. Reiserer, N. Kalb, M. S. Blok, J. Ruitenberg, R. F. L. Vermeulen, R. N. Schouten, C. Abellán, W. Amaya, V. Pruneri, M. W. Mitchell, M. Markham, D. J. Twitchen, D. Elkouss, S. Wehner, T. H. Taminiau, and R. Hanson, “Loophole-free Bell inequality violation using electron spins separated by 1.3 kilometres,” Nature 526, 682–686 (2015).
[Crossref] [PubMed]

Boas, C. J. V.

T. Werlang, S. Souza, F. F. Fanchini, and C. J. V. Boas, “Robustness of quantum discord to sudden death,” Phys. Rev. A 80, 024103 (2009).
[Crossref]

Bose, S.

M. Scala, M. S. Kim, G. W. Morley, P. F. Barker, and S. Bose, “Matter-wave interferometry of a levitated thermal nano-oscillator induced and probed by a spin,” Phys. Rev. Lett. 111, 180403 (2013).
[Crossref] [PubMed]

Boyer de lai Giroday, A.

S. Pironio, A. Acín, S. Massar, A. Boyer de lai Giroday, D. N. Matsukevich, P. Maunz, S. Olmschenk, D. Hayes, L. Luo, T. A. Manning, and C. Monroe, “Random numbers certified by Bell’s theorem,” Nature 464, 1021–1024 (2010).
[Crossref] [PubMed]

Branciard, C.

C. Branciard, N. Brunner, N. Gisin, C. Kurtsiefer, A. Lamas-Linares, A. Ling, and V. Scarani, “Testing quantum correlations versus single-particle properties within Leggett’s model and beyond,” Nat. Phys. 4, 681–685 (2008).
[Crossref]

C. Branciard, A. Ling, N. Gisin, C. Kurtsiefer, A. Lamas-Linares, and V. Scarani, “Experimental falsification of Leggett’s nonlocal variable model,” Phys. Rev. Lett. 99, 210407 (2007).
[Crossref]

Brendel, J.

W. Tittel, J. Brendel, B. Gisin, T. Herzog, H. Zbinden, and N. Gisin, “Experimental demonstration of quantum correlations over more than 10 km,” Phys. Rev. A 57, 3229 (1998).
[Crossref]

Brukner, C.

S. Gröblacher, T. Paterek, R. Kaltenbaek, Č. Brukner, M. Żukowski, M. Aspelmeyer, and A. Zeilinger, “An experimental test of non-local realism,” Nature 446, 871–875 (2007).
[Crossref] [PubMed]

Brunner, N.

M. T. Quintino, T. Vértesi, and N. Brunner, “Joint measurability, einstein-podolsky-rosen steering, and bell nonlocality,” Phys. Rev. Lett. 113, 160402 (2014).
[Crossref] [PubMed]

R. Rabelo, M. Ho, D. Cavalcanti, N. Brunner, and V. Scarani, “Device-independent certification of entangled measurements,” Phys. Rev. Lett. 107, 050502 (2011).
[Crossref] [PubMed]

C. Branciard, N. Brunner, N. Gisin, C. Kurtsiefer, A. Lamas-Linares, A. Ling, and V. Scarani, “Testing quantum correlations versus single-particle properties within Leggett’s model and beyond,” Nat. Phys. 4, 681–685 (2008).
[Crossref]

Buller, G. S.

A. C. Dada, J. Leach, G. S. Buller, M. J. Padgett, and E. Andersson, “Experimental high-dimensional two-photon entanglement and violations of generalized Bell inequalities,” Nat. Phys. 7, 677–680 (2011).
[Crossref]

Cao, Z. L.

X. L. Zhen, Q. Yang, M. Yang, and Z. L. Cao, “Bell-Nonlocality Dynamics of Three Remote Atoms in Tavis— Cummings and Jaynes—Cummings Models,” Commun. Theor. Phys. 62, 795–800 (2014).
[Crossref]

Cavalcanti, D.

R. Rabelo, M. Ho, D. Cavalcanti, N. Brunner, and V. Scarani, “Device-independent certification of entangled measurements,” Phys. Rev. Lett. 107, 050502 (2011).
[Crossref] [PubMed]

Chakrabarty, I.

P. Pandya, A. Misra, and I. Chakrabarty, “Complementarity between tripartite quantum correlation and bipartite Bell-inequality violation in three-qubit states,” Phys. Rev. A 94, 052126 (2016).
[Crossref]

Chen, J.

M. D. Eisaman, E. A. Goldschmidt, J. Chen, J. Fan, and A. Migdall, “Experimental test of nonlocal realism using a fiber-based source of polarization-entangled photon pairs,” Phys. Rev. A 77, 032339 (2008).
[Crossref]

Chen, R. X.

R. X. Chen, C. Hu, and L. Miao, “Dynamics of Bell-nonlocality of two-mode squeezed vacuum fields interacting with atoms,” Opt. Commun. 284, 2955–2959 (2011).
[Crossref]

Chen, X.-D.

X.-D. Chen, L.-M. Zhou, C.-L. Zou, C.-C. Li, Y. Dong, F.-W. Sun, and G.-C. Guo, “Spin depolarization effect induced by charge state conversion of nitrogen vacancy center in diamond,” Phys. Rev. B 92, 104301 (2015).
[Crossref]

Chen, Z. Q.

B. Wang, Z. Y. Xu, Z. Q. Chen, and M. Feng, “Non-Markovian effect on the quantum discord,” Phys. Rev. A 81, 014101 (2010).
[Crossref]

Chuang, I. L.

M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information (Cambridge University Press, 2000).

Clauser, J. F.

J. F. Clauser, M. A. Horne, A. Shimony, and R. A. Holt, “Proposed experiment to test local hidden-variable theories,” Phys. Rev. Lett. 23, 880 (1969).
[Crossref]

Cleland, A. N.

M. Ansmann, H. Wang, R. C. Bialczak, M. Hofheinz, E. Lucero, M. Neeley, A. D. O’Connell, D. Sank, M. Weides, J. Wenner, A. N. Cleland, and J. M. Martinis, “Violation of Bell’s inequality in Josephson phase qubits,” Nature 461, 504–506 (2009).
[Crossref] [PubMed]

Collins, D.

J. Barrett, D. Collins, L. Hardy, A. Kent, and S. Popescu, “Quantum nonlocality, Bell inequalities, and the memory loophole,” Phys. Rev. A 66, 042111 (2002).
[Crossref]

Compagno, G.

L. Mazzola, B. Bellomo, R. L. Franco, and G. Compagno, “Bell nonlocality in the turbulent atmosphere,” Phys. Rev. A 81, 052116 (2010).
[Crossref]

Dada, A. C.

A. C. Dada, J. Leach, G. S. Buller, M. J. Padgett, and E. Andersson, “Experimental high-dimensional two-photon entanglement and violations of generalized Bell inequalities,” Nat. Phys. 7, 677–680 (2011).
[Crossref]

Derkacz, L.

Ł. Derkacz and L. Jakobczyk, “Clauser-Horne-Shimony-Holt violation and the entropy-concurrence plane,” Phys. Rev. A 72, 042321 (2005).
[Crossref]

Dong, Y.

X.-D. Chen, L.-M. Zhou, C.-L. Zou, C.-C. Li, Y. Dong, F.-W. Sun, and G.-C. Guo, “Spin depolarization effect induced by charge state conversion of nitrogen vacancy center in diamond,” Phys. Rev. B 92, 104301 (2015).
[Crossref]

Dréau, A. E.

B. Hensen, N. Kalb, M. S. Blok, A. E. Dréau, A. Reiserer, R. F. L. Vermeulen, R. N. Schouten, M. Markham, D. J. Twitchen, K. Goodenough, D. Elkouss, S. Wehner, T. H. Taminiau, and R. Hansona, “Loophole-free Bell test using electron spins in diamond: second experiment and additional analysis,” Sci. Rep. 6, 30289 (2016).
[Crossref] [PubMed]

B. Hensen, H. Bernien, A. E. Dréau, A. Reiserer, N. Kalb, M. S. Blok, J. Ruitenberg, R. F. L. Vermeulen, R. N. Schouten, C. Abellán, W. Amaya, V. Pruneri, M. W. Mitchell, M. Markham, D. J. Twitchen, D. Elkouss, S. Wehner, T. H. Taminiau, and R. Hanson, “Loophole-free Bell inequality violation using electron spins separated by 1.3 kilometres,” Nature 526, 682–686 (2015).
[Crossref] [PubMed]

Duan, L. M.

Z. Yin, T. Li, X. Zhang, and L. M. Duan, “Large quantum superpositions of a levitated nanodiamond through spin-optomechanical coupling,” Phys. Rev. A 88, 033614 (2013).
[Crossref]

Dutta, A.

M. Żukowski, A. Dutta, and Z. Yin, “Geometric Bell-like inequalities for steering,” Phys. Rev. A 91, 032107 (2015).
[Crossref]

Eisaman, M. D.

M. D. Eisaman, E. A. Goldschmidt, J. Chen, J. Fan, and A. Migdall, “Experimental test of nonlocal realism using a fiber-based source of polarization-entangled photon pairs,” Phys. Rev. A 77, 032339 (2008).
[Crossref]

Elkouss, D.

B. Hensen, N. Kalb, M. S. Blok, A. E. Dréau, A. Reiserer, R. F. L. Vermeulen, R. N. Schouten, M. Markham, D. J. Twitchen, K. Goodenough, D. Elkouss, S. Wehner, T. H. Taminiau, and R. Hansona, “Loophole-free Bell test using electron spins in diamond: second experiment and additional analysis,” Sci. Rep. 6, 30289 (2016).
[Crossref] [PubMed]

B. Hensen, H. Bernien, A. E. Dréau, A. Reiserer, N. Kalb, M. S. Blok, J. Ruitenberg, R. F. L. Vermeulen, R. N. Schouten, C. Abellán, W. Amaya, V. Pruneri, M. W. Mitchell, M. Markham, D. J. Twitchen, D. Elkouss, S. Wehner, T. H. Taminiau, and R. Hanson, “Loophole-free Bell inequality violation using electron spins separated by 1.3 kilometres,” Nature 526, 682–686 (2015).
[Crossref] [PubMed]

Eryigit, R.

F. Altintas and R. Eryigit, “Quantum correlations in non-Markovian environments,” Phys. Lett. A 374, 4283 (2010).
[Crossref]

Eryigit, R. J.

F. Altintas and R. J. Eryigit, “Dynamics of entanglement and Bell non-locality for two stochastic qubits with dipole–dipole interaction,” J. Phys. A: Math. Theor. 43, 415306 (2010).
[Crossref]

Fan, J.

M. D. Eisaman, E. A. Goldschmidt, J. Chen, J. Fan, and A. Migdall, “Experimental test of nonlocal realism using a fiber-based source of polarization-entangled photon pairs,” Phys. Rev. A 77, 032339 (2008).
[Crossref]

Fanchini, F. F.

T. Werlang, S. Souza, F. F. Fanchini, and C. J. V. Boas, “Robustness of quantum discord to sudden death,” Phys. Rev. A 80, 024103 (2009).
[Crossref]

Fedrizzi, A.

T. Paterek, A. Fedrizzi, S. Gröblacher, T. Jennewein, M. Żukowski, M. Aspelmeyer, and A. Zeilinger, “Experimental test of nonlocal realistic theories without the rotational symmetry assumption,” Phys. Rev. Lett. 99, 210406 (2007).
[Crossref]

Feng, M.

B. Wang, Z. Y. Xu, Z. Q. Chen, and M. Feng, “Non-Markovian effect on the quantum discord,” Phys. Rev. A 81, 014101 (2010).
[Crossref]

Francica, F.

F. Francica, F. Plastina, and S. Maniscalco, “Quantum Zeno and anti-Zeno effects on quantum and classical correlations,” Phys. Rev. A 82, 052118 (2010).
[Crossref]

Franco, R. L.

L. Mazzola, B. Bellomo, R. L. Franco, and G. Compagno, “Bell nonlocality in the turbulent atmosphere,” Phys. Rev. A 81, 052116 (2010).
[Crossref]

Ge, R. C.

R. C. Ge, M. Gong, C. F. Li, J. S. Xu, and G. C. Guo, “Quantum correlation and classical correlation dynamics in the spin-boson model,” Phys. Rev. A 81, 064103 (2010).
[Crossref]

Gisin, B.

W. Tittel, J. Brendel, B. Gisin, T. Herzog, H. Zbinden, and N. Gisin, “Experimental demonstration of quantum correlations over more than 10 km,” Phys. Rev. A 57, 3229 (1998).
[Crossref]

Gisin, N.

C. Branciard, N. Brunner, N. Gisin, C. Kurtsiefer, A. Lamas-Linares, A. Ling, and V. Scarani, “Testing quantum correlations versus single-particle properties within Leggett’s model and beyond,” Nat. Phys. 4, 681–685 (2008).
[Crossref]

C. Branciard, A. Ling, N. Gisin, C. Kurtsiefer, A. Lamas-Linares, and V. Scarani, “Experimental falsification of Leggett’s nonlocal variable model,” Phys. Rev. Lett. 99, 210407 (2007).
[Crossref]

W. Tittel, J. Brendel, B. Gisin, T. Herzog, H. Zbinden, and N. Gisin, “Experimental demonstration of quantum correlations over more than 10 km,” Phys. Rev. A 57, 3229 (1998).
[Crossref]

N. Gisin, “Bell’s inequality holds for all non-product states,” Phys. Lett. A 154, 201–202 (1991).
[Crossref]

Glancy, S.

Y. Zhang, S. Glancy, and E. Knill, “Asymptotically optimal data analysis for rejecting local realism,” Phy. Rev. A 84, 062118 (2011).
[Crossref]

Goldschmidt, E. A.

M. D. Eisaman, E. A. Goldschmidt, J. Chen, J. Fan, and A. Migdall, “Experimental test of nonlocal realism using a fiber-based source of polarization-entangled photon pairs,” Phys. Rev. A 77, 032339 (2008).
[Crossref]

Gong, M.

R. C. Ge, M. Gong, C. F. Li, J. S. Xu, and G. C. Guo, “Quantum correlation and classical correlation dynamics in the spin-boson model,” Phys. Rev. A 81, 064103 (2010).
[Crossref]

Goodenough, K.

B. Hensen, N. Kalb, M. S. Blok, A. E. Dréau, A. Reiserer, R. F. L. Vermeulen, R. N. Schouten, M. Markham, D. J. Twitchen, K. Goodenough, D. Elkouss, S. Wehner, T. H. Taminiau, and R. Hansona, “Loophole-free Bell test using electron spins in diamond: second experiment and additional analysis,” Sci. Rep. 6, 30289 (2016).
[Crossref] [PubMed]

Gröblacher, S.

S. Gröblacher, T. Paterek, R. Kaltenbaek, Č. Brukner, M. Żukowski, M. Aspelmeyer, and A. Zeilinger, “An experimental test of non-local realism,” Nature 446, 871–875 (2007).
[Crossref] [PubMed]

T. Paterek, A. Fedrizzi, S. Gröblacher, T. Jennewein, M. Żukowski, M. Aspelmeyer, and A. Zeilinger, “Experimental test of nonlocal realistic theories without the rotational symmetry assumption,” Phys. Rev. Lett. 99, 210406 (2007).
[Crossref]

Gumberidze, M. O.

M. O. Gumberidze, A. A. Semenov, D. Vasylyev, and W. Vogel, “Bell nonlocality in the turbulent atmosphere,” Phys. Rev. A 94, 053801 (2016).
[Crossref]

Guo, G. C.

R. C. Ge, M. Gong, C. F. Li, J. S. Xu, and G. C. Guo, “Quantum correlation and classical correlation dynamics in the spin-boson model,” Phys. Rev. A 81, 064103 (2010).
[Crossref]

Guo, G.-C.

X.-D. Chen, L.-M. Zhou, C.-L. Zou, C.-C. Li, Y. Dong, F.-W. Sun, and G.-C. Guo, “Spin depolarization effect induced by charge state conversion of nitrogen vacancy center in diamond,” Phys. Rev. B 92, 104301 (2015).
[Crossref]

Hanson, R.

B. Hensen, H. Bernien, A. E. Dréau, A. Reiserer, N. Kalb, M. S. Blok, J. Ruitenberg, R. F. L. Vermeulen, R. N. Schouten, C. Abellán, W. Amaya, V. Pruneri, M. W. Mitchell, M. Markham, D. J. Twitchen, D. Elkouss, S. Wehner, T. H. Taminiau, and R. Hanson, “Loophole-free Bell inequality violation using electron spins separated by 1.3 kilometres,” Nature 526, 682–686 (2015).
[Crossref] [PubMed]

Hansona, R.

B. Hensen, N. Kalb, M. S. Blok, A. E. Dréau, A. Reiserer, R. F. L. Vermeulen, R. N. Schouten, M. Markham, D. J. Twitchen, K. Goodenough, D. Elkouss, S. Wehner, T. H. Taminiau, and R. Hansona, “Loophole-free Bell test using electron spins in diamond: second experiment and additional analysis,” Sci. Rep. 6, 30289 (2016).
[Crossref] [PubMed]

Hao, X.

X. Hao, C. L. Ma, and J. Sha, “Decoherence of quantum discord in an asymmetric-anisotropy spin system,” J. Phys. A: Math. Theor. 43, 425302 (2010).
[Crossref]

Hardy, L.

J. Barrett, D. Collins, L. Hardy, A. Kent, and S. Popescu, “Quantum nonlocality, Bell inequalities, and the memory loophole,” Phys. Rev. A 66, 042111 (2002).
[Crossref]

Harris, J. G. E.

S. Kolkowitz, A. C. B. Jayich, Q. P. Unterreithmeier, S. D. Bennett, P. Rabl, J. G. E. Harris, and M. D. Lukin, “Coherent sensing of a mechanical resonator with a single-spin qubit,” Science 335, 1603–1606 (2012).
[Crossref] [PubMed]

Hayes, D.

S. Pironio, A. Acín, S. Massar, A. Boyer de lai Giroday, D. N. Matsukevich, P. Maunz, S. Olmschenk, D. Hayes, L. Luo, T. A. Manning, and C. Monroe, “Random numbers certified by Bell’s theorem,” Nature 464, 1021–1024 (2010).
[Crossref] [PubMed]

Hensen, B.

B. Hensen, N. Kalb, M. S. Blok, A. E. Dréau, A. Reiserer, R. F. L. Vermeulen, R. N. Schouten, M. Markham, D. J. Twitchen, K. Goodenough, D. Elkouss, S. Wehner, T. H. Taminiau, and R. Hansona, “Loophole-free Bell test using electron spins in diamond: second experiment and additional analysis,” Sci. Rep. 6, 30289 (2016).
[Crossref] [PubMed]

B. Hensen, H. Bernien, A. E. Dréau, A. Reiserer, N. Kalb, M. S. Blok, J. Ruitenberg, R. F. L. Vermeulen, R. N. Schouten, C. Abellán, W. Amaya, V. Pruneri, M. W. Mitchell, M. Markham, D. J. Twitchen, D. Elkouss, S. Wehner, T. H. Taminiau, and R. Hanson, “Loophole-free Bell inequality violation using electron spins separated by 1.3 kilometres,” Nature 526, 682–686 (2015).
[Crossref] [PubMed]

Herzog, T.

W. Tittel, J. Brendel, B. Gisin, T. Herzog, H. Zbinden, and N. Gisin, “Experimental demonstration of quantum correlations over more than 10 km,” Phys. Rev. A 57, 3229 (1998).
[Crossref]

Ho, M.

R. Rabelo, M. Ho, D. Cavalcanti, N. Brunner, and V. Scarani, “Device-independent certification of entangled measurements,” Phys. Rev. Lett. 107, 050502 (2011).
[Crossref] [PubMed]

Ho, S.-W.

N. Zhao, J.-L. Hu, S.-W. Ho, J. T. K. Wan, and R. B. Liu, “Atomic-scale magnetometry of distant nuclear spin clusters via nitrogen-vacancy spin in diamond,” Nat. Nanotech. 6, 242–246 (2011).
[Crossref]

Hofheinz, M.

M. Ansmann, H. Wang, R. C. Bialczak, M. Hofheinz, E. Lucero, M. Neeley, A. D. O’Connell, D. Sank, M. Weides, J. Wenner, A. N. Cleland, and J. M. Martinis, “Violation of Bell’s inequality in Josephson phase qubits,” Nature 461, 504–506 (2009).
[Crossref] [PubMed]

Holt, R. A.

J. F. Clauser, M. A. Horne, A. Shimony, and R. A. Holt, “Proposed experiment to test local hidden-variable theories,” Phys. Rev. Lett. 23, 880 (1969).
[Crossref]

Horne, M. A.

J. F. Clauser, M. A. Horne, A. Shimony, and R. A. Holt, “Proposed experiment to test local hidden-variable theories,” Phys. Rev. Lett. 23, 880 (1969).
[Crossref]

Horodecki, M.

R. Horodecki, P. Horodecki, and M. Horodecki, “Violating Bell inequality by mixed spin-12 states: necessary and sufficient condition,” Phys. Lett. A 200, 340–344 (1995).
[Crossref]

Horodecki, P.

R. Horodecki, P. Horodecki, and M. Horodecki, “Violating Bell inequality by mixed spin-12 states: necessary and sufficient condition,” Phys. Lett. A 200, 340–344 (1995).
[Crossref]

Horodecki, R.

R. Horodecki, “Two-spin-12 mixtures and Bell’s inequalities,” Phys. Lett. A 210, 223–226 (1996).
[Crossref]

R. Horodecki, P. Horodecki, and M. Horodecki, “Violating Bell inequality by mixed spin-12 states: necessary and sufficient condition,” Phys. Lett. A 200, 340–344 (1995).
[Crossref]

Hu, C.

R. X. Chen, C. Hu, and L. Miao, “Dynamics of Bell-nonlocality of two-mode squeezed vacuum fields interacting with atoms,” Opt. Commun. 284, 2955–2959 (2011).
[Crossref]

Hu, J.-L.

N. Zhao, J.-L. Hu, S.-W. Ho, J. T. K. Wan, and R. B. Liu, “Atomic-scale magnetometry of distant nuclear spin clusters via nitrogen-vacancy spin in diamond,” Nat. Nanotech. 6, 242–246 (2011).
[Crossref]

Huelga, S. F.

G. Waldherr, P. Neumann, S. F. Huelga, F. Jelezko, and J. Wrachtrup, “Violation of a temporal Bell inequality for single spins in a diamond defect center,” Phys. Rev. Lett. 107, 090401 (2011).
[Crossref] [PubMed]

Ikeda, T.

H. Sakai, T. Saito, T. Ikeda, K. Itoh, T. Kawabata, H. Kuboki, Y. Maeda, N. Matsui, C. Rangacharyulu, M. Sasano, Y. Satou, K. Sekiguchi, K. Suda, A. Tamii, T. Uesaka, and K. Yako, “Spin correlations of strongly interacting massive fermion pairs as a test of Bell’s inequality,” Phys. Rev. Lett. 97, 150405 (2006).
[Crossref]

Itano, W. M.

M. A. Rowe, D. Kielpinski, V. Meyer, C. A. Sackett, W. M. Itano, C. Monroe, and D. J. Wineland, “Experimental violation of a Bell’s inequality with efficient detection,” Nature 409, 791–794 (2001).
[Crossref] [PubMed]

Itoh, K.

H. Sakai, T. Saito, T. Ikeda, K. Itoh, T. Kawabata, H. Kuboki, Y. Maeda, N. Matsui, C. Rangacharyulu, M. Sasano, Y. Satou, K. Sekiguchi, K. Suda, A. Tamii, T. Uesaka, and K. Yako, “Spin correlations of strongly interacting massive fermion pairs as a test of Bell’s inequality,” Phys. Rev. Lett. 97, 150405 (2006).
[Crossref]

Jaeger, G.

G. Jaeger, Entanglement, Information, and the Interpretation of Quantum Mechanics (Springer, 2010).

Jakobczyk, L.

Ł. Derkacz and L. Jakobczyk, “Clauser-Horne-Shimony-Holt violation and the entropy-concurrence plane,” Phys. Rev. A 72, 042321 (2005).
[Crossref]

Jayich, A. C. B.

S. Kolkowitz, A. C. B. Jayich, Q. P. Unterreithmeier, S. D. Bennett, P. Rabl, J. G. E. Harris, and M. D. Lukin, “Coherent sensing of a mechanical resonator with a single-spin qubit,” Science 335, 1603–1606 (2012).
[Crossref] [PubMed]

Jelezko, F.

G. Waldherr, P. Neumann, S. F. Huelga, F. Jelezko, and J. Wrachtrup, “Violation of a temporal Bell inequality for single spins in a diamond defect center,” Phys. Rev. Lett. 107, 090401 (2011).
[Crossref] [PubMed]

Jennewein, T.

T. Paterek, A. Fedrizzi, S. Gröblacher, T. Jennewein, M. Żukowski, M. Aspelmeyer, and A. Zeilinger, “Experimental test of nonlocal realistic theories without the rotational symmetry assumption,” Phys. Rev. Lett. 99, 210406 (2007).
[Crossref]

G. Weihs, T. Jennewein, C. Simon, H. Weinfurter, and A. Zeilinger, “Violation of Bell’s inequality under strict Einstein locality conditions,” Phys. Rev. Lett. 81, 5039 (1998).
[Crossref]

Jeong, H.

C.-W. Lee, M. Paternostro, and H. Jeong, “Faithful test of nonlocal realism with entangled coherent states,” Phys. Rev. A 83, 022102 (2011).
[Crossref]

M. Paternostro and H. Jeong, “Testing nonlocal realism with entangled coherent states,” Phys. Rev. A 81, 032115 (2010).
[Crossref]

Kalb, N.

B. Hensen, N. Kalb, M. S. Blok, A. E. Dréau, A. Reiserer, R. F. L. Vermeulen, R. N. Schouten, M. Markham, D. J. Twitchen, K. Goodenough, D. Elkouss, S. Wehner, T. H. Taminiau, and R. Hansona, “Loophole-free Bell test using electron spins in diamond: second experiment and additional analysis,” Sci. Rep. 6, 30289 (2016).
[Crossref] [PubMed]

B. Hensen, H. Bernien, A. E. Dréau, A. Reiserer, N. Kalb, M. S. Blok, J. Ruitenberg, R. F. L. Vermeulen, R. N. Schouten, C. Abellán, W. Amaya, V. Pruneri, M. W. Mitchell, M. Markham, D. J. Twitchen, D. Elkouss, S. Wehner, T. H. Taminiau, and R. Hanson, “Loophole-free Bell inequality violation using electron spins separated by 1.3 kilometres,” Nature 526, 682–686 (2015).
[Crossref] [PubMed]

Kaltenbaek, R.

S. Gröblacher, T. Paterek, R. Kaltenbaek, Č. Brukner, M. Żukowski, M. Aspelmeyer, and A. Zeilinger, “An experimental test of non-local realism,” Nature 446, 871–875 (2007).
[Crossref] [PubMed]

Kaszlikowski, D.

M. Pawlowski, T. Paterek, D. Kaszlikowski, V. Scarani, A. Winter, and M. Zukowski, “Information causality as a physical principle,” Nature 461, 1101–1104 (2009).
[Crossref] [PubMed]

Kawabata, T.

H. Sakai, T. Saito, T. Ikeda, K. Itoh, T. Kawabata, H. Kuboki, Y. Maeda, N. Matsui, C. Rangacharyulu, M. Sasano, Y. Satou, K. Sekiguchi, K. Suda, A. Tamii, T. Uesaka, and K. Yako, “Spin correlations of strongly interacting massive fermion pairs as a test of Bell’s inequality,” Phys. Rev. Lett. 97, 150405 (2006).
[Crossref]

Kent, A.

J. Barrett, D. Collins, L. Hardy, A. Kent, and S. Popescu, “Quantum nonlocality, Bell inequalities, and the memory loophole,” Phys. Rev. A 66, 042111 (2002).
[Crossref]

Kielpinski, D.

M. A. Rowe, D. Kielpinski, V. Meyer, C. A. Sackett, W. M. Itano, C. Monroe, and D. J. Wineland, “Experimental violation of a Bell’s inequality with efficient detection,” Nature 409, 791–794 (2001).
[Crossref] [PubMed]

Kim, M. S.

M. Scala, M. S. Kim, G. W. Morley, P. F. Barker, and S. Bose, “Matter-wave interferometry of a levitated thermal nano-oscillator induced and probed by a spin,” Phys. Rev. Lett. 111, 180403 (2013).
[Crossref] [PubMed]

M. S. Kim, J. Lee, D. Ahn, and P. L. Knight, “Entanglement induced by a single-mode heat environment,” Phys. Rev. A 65, 040101 (2002).
[Crossref]

Knight, P. L.

M. S. Kim, J. Lee, D. Ahn, and P. L. Knight, “Entanglement induced by a single-mode heat environment,” Phys. Rev. A 65, 040101 (2002).
[Crossref]

Knill, E.

Y. Zhang, S. Glancy, and E. Knill, “Asymptotically optimal data analysis for rejecting local realism,” Phy. Rev. A 84, 062118 (2011).
[Crossref]

Kofman, A. G.

A. G. Kofman and A. N. Korotkov, “Bell-inequality violation versus entanglement in the presence of local decoherence,” Phys. Rev. A 77, 052329 (2008).
[Crossref]

Kolkowitz, S.

S. Kolkowitz, A. C. B. Jayich, Q. P. Unterreithmeier, S. D. Bennett, P. Rabl, J. G. E. Harris, and M. D. Lukin, “Coherent sensing of a mechanical resonator with a single-spin qubit,” Science 335, 1603–1606 (2012).
[Crossref] [PubMed]

Korotkov, A. N.

A. G. Kofman and A. N. Korotkov, “Bell-inequality violation versus entanglement in the presence of local decoherence,” Phys. Rev. A 77, 052329 (2008).
[Crossref]

Kuang, L. M.

J. B. Yuan, L. M. Kuang, and J. Q. Liao, “Amplification of quantum discord between two uncoupled qubits in a common environment by phase decoherence,” J. Phys. B: At. Mol. Opt. Phys. 43, 165503 (2010).
[Crossref]

Kuboki, H.

H. Sakai, T. Saito, T. Ikeda, K. Itoh, T. Kawabata, H. Kuboki, Y. Maeda, N. Matsui, C. Rangacharyulu, M. Sasano, Y. Satou, K. Sekiguchi, K. Suda, A. Tamii, T. Uesaka, and K. Yako, “Spin correlations of strongly interacting massive fermion pairs as a test of Bell’s inequality,” Phys. Rev. Lett. 97, 150405 (2006).
[Crossref]

Kurtsiefer, C.

C. Branciard, N. Brunner, N. Gisin, C. Kurtsiefer, A. Lamas-Linares, A. Ling, and V. Scarani, “Testing quantum correlations versus single-particle properties within Leggett’s model and beyond,” Nat. Phys. 4, 681–685 (2008).
[Crossref]

C. Branciard, A. Ling, N. Gisin, C. Kurtsiefer, A. Lamas-Linares, and V. Scarani, “Experimental falsification of Leggett’s nonlocal variable model,” Phys. Rev. Lett. 99, 210407 (2007).
[Crossref]

Kwiat, P. G.

P. G. Kwiat, K. Mattle, H. Weinfurter, A. Zeilinger, A. V. Sergienko, and Y. Shih, “New high-intensity source of polarization-entangled photon pairs,” Phy. Rev. Lett. 75, 4337 (1995).
[Crossref]

Lamas-Linares, A.

C. Branciard, N. Brunner, N. Gisin, C. Kurtsiefer, A. Lamas-Linares, A. Ling, and V. Scarani, “Testing quantum correlations versus single-particle properties within Leggett’s model and beyond,” Nat. Phys. 4, 681–685 (2008).
[Crossref]

C. Branciard, A. Ling, N. Gisin, C. Kurtsiefer, A. Lamas-Linares, and V. Scarani, “Experimental falsification of Leggett’s nonlocal variable model,” Phys. Rev. Lett. 99, 210407 (2007).
[Crossref]

Leach, J.

A. C. Dada, J. Leach, G. S. Buller, M. J. Padgett, and E. Andersson, “Experimental high-dimensional two-photon entanglement and violations of generalized Bell inequalities,” Nat. Phys. 7, 677–680 (2011).
[Crossref]

Lee, C.-W.

C.-W. Lee, M. Paternostro, and H. Jeong, “Faithful test of nonlocal realism with entangled coherent states,” Phys. Rev. A 83, 022102 (2011).
[Crossref]

Lee, J.

M. S. Kim, J. Lee, D. Ahn, and P. L. Knight, “Entanglement induced by a single-mode heat environment,” Phys. Rev. A 65, 040101 (2002).
[Crossref]

Leggett, A. J.

A. J. Leggett, “Nonlocal hidden-variable theories and quantum mechanics: An incompatibility theorem,” Found. Phys. 33, 1469–1493 (2003).
[Crossref]

Li, C. F.

R. C. Ge, M. Gong, C. F. Li, J. S. Xu, and G. C. Guo, “Quantum correlation and classical correlation dynamics in the spin-boson model,” Phys. Rev. A 81, 064103 (2010).
[Crossref]

Li, C.-C.

X.-D. Chen, L.-M. Zhou, C.-L. Zou, C.-C. Li, Y. Dong, F.-W. Sun, and G.-C. Guo, “Spin depolarization effect induced by charge state conversion of nitrogen vacancy center in diamond,” Phys. Rev. B 92, 104301 (2015).
[Crossref]

Li, J. Q.

J. Q. Li and J. Q. Liang, “Disentanglement and Bell nonlocality in a classical dephasing environment,” Phys. Lett. A 374, 1975–1979 (2010).
[Crossref]

Li, S. B.

S. B. Li and J. B. Xu, “Entanglement, Bell violation, and phase decoherence of two atoms inside an optical cavity,” Phys. Rev. A 72, 022332 (2005).
[Crossref]

Li, S.-B.

J.-B. Xu and S.-B. Li, “Control of the entanglement of two atoms in an optical cavity via white noise,” New J. Phys. 7, 72 (2005).
[Crossref]

Li, T.

Z. Yin, T. Li, X. Zhang, and L. M. Duan, “Large quantum superpositions of a levitated nanodiamond through spin-optomechanical coupling,” Phys. Rev. A 88, 033614 (2013).
[Crossref]

Lian, J. L.

Z. M. Wang, J. L. Lian, J.-Q. Liang, W-M Liu, and Y. M. Yu, “Collapse of the superradiant phase and multiple quantum phase transitions for Bose-Einstein condensates in an optomechanical cavity,” Phys. Rev. A 93, 033630 (2016).
[Crossref]

Liang, J. Q.

J. Q. Li and J. Q. Liang, “Disentanglement and Bell nonlocality in a classical dephasing environment,” Phys. Lett. A 374, 1975–1979 (2010).
[Crossref]

Liang, J.-Q.

H. F. Zhang, J. H. Wang, Z. G. Song, J.-Q. Liang, and L.-F. Wei, “Spin-parity effect in violation of bell’s inequalities for entangled states of parallel polarization,” Mod. Phys. Lett. B 31, 1750032 (2017).
[Crossref]

Z. M. Wang, J. L. Lian, J.-Q. Liang, W-M Liu, and Y. M. Yu, “Collapse of the superradiant phase and multiple quantum phase transitions for Bose-Einstein condensates in an optomechanical cavity,” Phys. Rev. A 93, 033630 (2016).
[Crossref]

M. H. Wang, L. F. Wei, and J.-Q. Liang, “Does the Berry phase in a quantum optical system originate from the rotating wave approximation,” Phys. Lett. A 379, 1087–1090 (2015).
[Crossref]

X. Q. Zhao, N. Liu, and J.-Q. Liang, “Nonlinear atom-photon-interaction-induced population inversion and inverted quantum phase transition of Bose-Einstein condensate in an optical cavity,” Phys. Rev. A 90, 023622 (2014).
[Crossref]

Z. Song, J.-Q. Liang, and L.-F. Wei, “Spin-Parity Effect in Violation of Bell’s Inequalities,” Mod. Phys. Lett. B 28, 1450004 (2014).
[Crossref]

Liao, J. Q.

J. B. Yuan, L. M. Kuang, and J. Q. Liao, “Amplification of quantum discord between two uncoupled qubits in a common environment by phase decoherence,” J. Phys. B: At. Mol. Opt. Phys. 43, 165503 (2010).
[Crossref]

Ling, A.

C. Branciard, N. Brunner, N. Gisin, C. Kurtsiefer, A. Lamas-Linares, A. Ling, and V. Scarani, “Testing quantum correlations versus single-particle properties within Leggett’s model and beyond,” Nat. Phys. 4, 681–685 (2008).
[Crossref]

C. Branciard, A. Ling, N. Gisin, C. Kurtsiefer, A. Lamas-Linares, and V. Scarani, “Experimental falsification of Leggett’s nonlocal variable model,” Phys. Rev. Lett. 99, 210407 (2007).
[Crossref]

Liu, N.

X. Q. Zhao, N. Liu, and J.-Q. Liang, “Nonlinear atom-photon-interaction-induced population inversion and inverted quantum phase transition of Bose-Einstein condensate in an optical cavity,” Phys. Rev. A 90, 023622 (2014).
[Crossref]

Liu, R. B.

N. Zhao, J.-L. Hu, S.-W. Ho, J. T. K. Wan, and R. B. Liu, “Atomic-scale magnetometry of distant nuclear spin clusters via nitrogen-vacancy spin in diamond,” Nat. Nanotech. 6, 242–246 (2011).
[Crossref]

Liu, W-M

Z. M. Wang, J. L. Lian, J.-Q. Liang, W-M Liu, and Y. M. Yu, “Collapse of the superradiant phase and multiple quantum phase transitions for Bose-Einstein condensates in an optomechanical cavity,” Phys. Rev. A 93, 033630 (2016).
[Crossref]

Liu, Y. X.

L. F. Wei, Y. X. Liu, and F. Nori, “Testing Bell’s inequality in a constantly coupled Josephson circuit by effective single-qubit operations,” Phys. Rev. B 72, 104516 (2005).
[Crossref]

Lu, X. M.

Z. Sun, X. M. Lu, and L. J. Song, “Quantum discord induced by a spin chain with quantum phase transition,” J. Phys. B: At. Mol. Opt. Phys. 43, 215504 (2010).
[Crossref]

X. M. Lu, Z. Xi, Z. Sun, and X. Wang, “Geometric measure of quantum discord under decoherence,” Quantum Inf. Comput. 10, 994–1003 (2010).

Lucero, E.

M. Ansmann, H. Wang, R. C. Bialczak, M. Hofheinz, E. Lucero, M. Neeley, A. D. O’Connell, D. Sank, M. Weides, J. Wenner, A. N. Cleland, and J. M. Martinis, “Violation of Bell’s inequality in Josephson phase qubits,” Nature 461, 504–506 (2009).
[Crossref] [PubMed]

Lukin, M. D.

S. Kolkowitz, A. C. B. Jayich, Q. P. Unterreithmeier, S. D. Bennett, P. Rabl, J. G. E. Harris, and M. D. Lukin, “Coherent sensing of a mechanical resonator with a single-spin qubit,” Science 335, 1603–1606 (2012).
[Crossref] [PubMed]

Luo, L.

S. Pironio, A. Acín, S. Massar, A. Boyer de lai Giroday, D. N. Matsukevich, P. Maunz, S. Olmschenk, D. Hayes, L. Luo, T. A. Manning, and C. Monroe, “Random numbers certified by Bell’s theorem,” Nature 464, 1021–1024 (2010).
[Crossref] [PubMed]

Ma, C. L.

X. Hao, C. L. Ma, and J. Sha, “Decoherence of quantum discord in an asymmetric-anisotropy spin system,” J. Phys. A: Math. Theor. 43, 425302 (2010).
[Crossref]

Maeda, Y.

H. Sakai, T. Saito, T. Ikeda, K. Itoh, T. Kawabata, H. Kuboki, Y. Maeda, N. Matsui, C. Rangacharyulu, M. Sasano, Y. Satou, K. Sekiguchi, K. Suda, A. Tamii, T. Uesaka, and K. Yako, “Spin correlations of strongly interacting massive fermion pairs as a test of Bell’s inequality,” Phys. Rev. Lett. 97, 150405 (2006).
[Crossref]

Maniscalco, S.

F. Francica, F. Plastina, and S. Maniscalco, “Quantum Zeno and anti-Zeno effects on quantum and classical correlations,” Phys. Rev. A 82, 052118 (2010).
[Crossref]

Manning, T. A.

S. Pironio, A. Acín, S. Massar, A. Boyer de lai Giroday, D. N. Matsukevich, P. Maunz, S. Olmschenk, D. Hayes, L. Luo, T. A. Manning, and C. Monroe, “Random numbers certified by Bell’s theorem,” Nature 464, 1021–1024 (2010).
[Crossref] [PubMed]

Markham, M.

B. Hensen, N. Kalb, M. S. Blok, A. E. Dréau, A. Reiserer, R. F. L. Vermeulen, R. N. Schouten, M. Markham, D. J. Twitchen, K. Goodenough, D. Elkouss, S. Wehner, T. H. Taminiau, and R. Hansona, “Loophole-free Bell test using electron spins in diamond: second experiment and additional analysis,” Sci. Rep. 6, 30289 (2016).
[Crossref] [PubMed]

B. Hensen, H. Bernien, A. E. Dréau, A. Reiserer, N. Kalb, M. S. Blok, J. Ruitenberg, R. F. L. Vermeulen, R. N. Schouten, C. Abellán, W. Amaya, V. Pruneri, M. W. Mitchell, M. Markham, D. J. Twitchen, D. Elkouss, S. Wehner, T. H. Taminiau, and R. Hanson, “Loophole-free Bell inequality violation using electron spins separated by 1.3 kilometres,” Nature 526, 682–686 (2015).
[Crossref] [PubMed]

Martinis, J. M.

M. Ansmann, H. Wang, R. C. Bialczak, M. Hofheinz, E. Lucero, M. Neeley, A. D. O’Connell, D. Sank, M. Weides, J. Wenner, A. N. Cleland, and J. M. Martinis, “Violation of Bell’s inequality in Josephson phase qubits,” Nature 461, 504–506 (2009).
[Crossref] [PubMed]

Massar, S.

S. Pironio, A. Acín, S. Massar, A. Boyer de lai Giroday, D. N. Matsukevich, P. Maunz, S. Olmschenk, D. Hayes, L. Luo, T. A. Manning, and C. Monroe, “Random numbers certified by Bell’s theorem,” Nature 464, 1021–1024 (2010).
[Crossref] [PubMed]

Matsui, N.

H. Sakai, T. Saito, T. Ikeda, K. Itoh, T. Kawabata, H. Kuboki, Y. Maeda, N. Matsui, C. Rangacharyulu, M. Sasano, Y. Satou, K. Sekiguchi, K. Suda, A. Tamii, T. Uesaka, and K. Yako, “Spin correlations of strongly interacting massive fermion pairs as a test of Bell’s inequality,” Phys. Rev. Lett. 97, 150405 (2006).
[Crossref]

Matsukevich, D. N.

S. Pironio, A. Acín, S. Massar, A. Boyer de lai Giroday, D. N. Matsukevich, P. Maunz, S. Olmschenk, D. Hayes, L. Luo, T. A. Manning, and C. Monroe, “Random numbers certified by Bell’s theorem,” Nature 464, 1021–1024 (2010).
[Crossref] [PubMed]

Mattle, K.

P. G. Kwiat, K. Mattle, H. Weinfurter, A. Zeilinger, A. V. Sergienko, and Y. Shih, “New high-intensity source of polarization-entangled photon pairs,” Phy. Rev. Lett. 75, 4337 (1995).
[Crossref]

Maunz, P.

S. Pironio, A. Acín, S. Massar, A. Boyer de lai Giroday, D. N. Matsukevich, P. Maunz, S. Olmschenk, D. Hayes, L. Luo, T. A. Manning, and C. Monroe, “Random numbers certified by Bell’s theorem,” Nature 464, 1021–1024 (2010).
[Crossref] [PubMed]

Mazzola, L.

L. Mazzola, B. Bellomo, R. L. Franco, and G. Compagno, “Bell nonlocality in the turbulent atmosphere,” Phys. Rev. A 81, 052116 (2010).
[Crossref]

Meyer, V.

M. A. Rowe, D. Kielpinski, V. Meyer, C. A. Sackett, W. M. Itano, C. Monroe, and D. J. Wineland, “Experimental violation of a Bell’s inequality with efficient detection,” Nature 409, 791–794 (2001).
[Crossref] [PubMed]

Miao, L.

R. X. Chen, C. Hu, and L. Miao, “Dynamics of Bell-nonlocality of two-mode squeezed vacuum fields interacting with atoms,” Opt. Commun. 284, 2955–2959 (2011).
[Crossref]

Migdall, A.

M. D. Eisaman, E. A. Goldschmidt, J. Chen, J. Fan, and A. Migdall, “Experimental test of nonlocal realism using a fiber-based source of polarization-entangled photon pairs,” Phys. Rev. A 77, 032339 (2008).
[Crossref]

Milburn, G. J.

T. M. Stace, G. J. Milburn, and C. H. W. Barnes, “Entangled two-photon source using biexciton emission of an asymmetric quantum dot in a cavity,” Phys. Rev. B 67, 085317 (2003).
[Crossref]

Misra, A.

P. Pandya, A. Misra, and I. Chakrabarty, “Complementarity between tripartite quantum correlation and bipartite Bell-inequality violation in three-qubit states,” Phys. Rev. A 94, 052126 (2016).
[Crossref]

Mitchell, M. W.

B. Hensen, H. Bernien, A. E. Dréau, A. Reiserer, N. Kalb, M. S. Blok, J. Ruitenberg, R. F. L. Vermeulen, R. N. Schouten, C. Abellán, W. Amaya, V. Pruneri, M. W. Mitchell, M. Markham, D. J. Twitchen, D. Elkouss, S. Wehner, T. H. Taminiau, and R. Hanson, “Loophole-free Bell inequality violation using electron spins separated by 1.3 kilometres,” Nature 526, 682–686 (2015).
[Crossref] [PubMed]

Monroe, C.

S. Pironio, A. Acín, S. Massar, A. Boyer de lai Giroday, D. N. Matsukevich, P. Maunz, S. Olmschenk, D. Hayes, L. Luo, T. A. Manning, and C. Monroe, “Random numbers certified by Bell’s theorem,” Nature 464, 1021–1024 (2010).
[Crossref] [PubMed]

M. A. Rowe, D. Kielpinski, V. Meyer, C. A. Sackett, W. M. Itano, C. Monroe, and D. J. Wineland, “Experimental violation of a Bell’s inequality with efficient detection,” Nature 409, 791–794 (2001).
[Crossref] [PubMed]

Morley, G. W.

M. Scala, M. S. Kim, G. W. Morley, P. F. Barker, and S. Bose, “Matter-wave interferometry of a levitated thermal nano-oscillator induced and probed by a spin,” Phys. Rev. Lett. 111, 180403 (2013).
[Crossref] [PubMed]

Mukherjee, A.

A. Roy, S. S. Bhattacharya, A. Mukherjee, and M. Banik, “Optimal quantum violation of Clauser-Horne-Shimony-Holt like steering inequality,” J. Phys. A 48, 415302 (2015).
[Crossref]

Neeley, M.

M. Ansmann, H. Wang, R. C. Bialczak, M. Hofheinz, E. Lucero, M. Neeley, A. D. O’Connell, D. Sank, M. Weides, J. Wenner, A. N. Cleland, and J. M. Martinis, “Violation of Bell’s inequality in Josephson phase qubits,” Nature 461, 504–506 (2009).
[Crossref] [PubMed]

Neumann, P.

G. Waldherr, P. Neumann, S. F. Huelga, F. Jelezko, and J. Wrachtrup, “Violation of a temporal Bell inequality for single spins in a diamond defect center,” Phys. Rev. Lett. 107, 090401 (2011).
[Crossref] [PubMed]

Nielsen, M. A.

M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information (Cambridge University Press, 2000).

Nori, F.

L. F. Wei, Y. X. Liu, and F. Nori, “Testing Bell’s inequality in a constantly coupled Josephson circuit by effective single-qubit operations,” Phys. Rev. B 72, 104516 (2005).
[Crossref]

O’Connell, A. D.

M. Ansmann, H. Wang, R. C. Bialczak, M. Hofheinz, E. Lucero, M. Neeley, A. D. O’Connell, D. Sank, M. Weides, J. Wenner, A. N. Cleland, and J. M. Martinis, “Violation of Bell’s inequality in Josephson phase qubits,” Nature 461, 504–506 (2009).
[Crossref] [PubMed]

Olmschenk, S.

S. Pironio, A. Acín, S. Massar, A. Boyer de lai Giroday, D. N. Matsukevich, P. Maunz, S. Olmschenk, D. Hayes, L. Luo, T. A. Manning, and C. Monroe, “Random numbers certified by Bell’s theorem,” Nature 464, 1021–1024 (2010).
[Crossref] [PubMed]

Padgett, M. J.

A. C. Dada, J. Leach, G. S. Buller, M. J. Padgett, and E. Andersson, “Experimental high-dimensional two-photon entanglement and violations of generalized Bell inequalities,” Nat. Phys. 7, 677–680 (2011).
[Crossref]

Pandya, P.

P. Pandya, A. Misra, and I. Chakrabarty, “Complementarity between tripartite quantum correlation and bipartite Bell-inequality violation in three-qubit states,” Phys. Rev. A 94, 052126 (2016).
[Crossref]

Paterek, T.

M. Pawlowski, T. Paterek, D. Kaszlikowski, V. Scarani, A. Winter, and M. Zukowski, “Information causality as a physical principle,” Nature 461, 1101–1104 (2009).
[Crossref] [PubMed]

T. Paterek, A. Fedrizzi, S. Gröblacher, T. Jennewein, M. Żukowski, M. Aspelmeyer, and A. Zeilinger, “Experimental test of nonlocal realistic theories without the rotational symmetry assumption,” Phys. Rev. Lett. 99, 210406 (2007).
[Crossref]

S. Gröblacher, T. Paterek, R. Kaltenbaek, Č. Brukner, M. Żukowski, M. Aspelmeyer, and A. Zeilinger, “An experimental test of non-local realism,” Nature 446, 871–875 (2007).
[Crossref] [PubMed]

Paternostro, M.

C.-W. Lee, M. Paternostro, and H. Jeong, “Faithful test of nonlocal realism with entangled coherent states,” Phys. Rev. A 83, 022102 (2011).
[Crossref]

M. Paternostro and H. Jeong, “Testing nonlocal realism with entangled coherent states,” Phys. Rev. A 81, 032115 (2010).
[Crossref]

Pawlowski, M.

M. Pawlowski, T. Paterek, D. Kaszlikowski, V. Scarani, A. Winter, and M. Zukowski, “Information causality as a physical principle,” Nature 461, 1101–1104 (2009).
[Crossref] [PubMed]

Pironio, S.

S. Pironio, A. Acín, S. Massar, A. Boyer de lai Giroday, D. N. Matsukevich, P. Maunz, S. Olmschenk, D. Hayes, L. Luo, T. A. Manning, and C. Monroe, “Random numbers certified by Bell’s theorem,” Nature 464, 1021–1024 (2010).
[Crossref] [PubMed]

Plastina, F.

F. Francica, F. Plastina, and S. Maniscalco, “Quantum Zeno and anti-Zeno effects on quantum and classical correlations,” Phys. Rev. A 82, 052118 (2010).
[Crossref]

Polozova, E.

E. Polozova and F. W. Strauch, “Higher-dimensional Bell inequalities with noisy qudits,” Phys. Rev. A 93, 032130 (2016).
[Crossref]

Popescu, S.

J. Barrett, D. Collins, L. Hardy, A. Kent, and S. Popescu, “Quantum nonlocality, Bell inequalities, and the memory loophole,” Phys. Rev. A 66, 042111 (2002).
[Crossref]

Pruneri, V.

B. Hensen, H. Bernien, A. E. Dréau, A. Reiserer, N. Kalb, M. S. Blok, J. Ruitenberg, R. F. L. Vermeulen, R. N. Schouten, C. Abellán, W. Amaya, V. Pruneri, M. W. Mitchell, M. Markham, D. J. Twitchen, D. Elkouss, S. Wehner, T. H. Taminiau, and R. Hanson, “Loophole-free Bell inequality violation using electron spins separated by 1.3 kilometres,” Nature 526, 682–686 (2015).
[Crossref] [PubMed]

Quintino, M. T.

M. T. Quintino, T. Vértesi, and N. Brunner, “Joint measurability, einstein-podolsky-rosen steering, and bell nonlocality,” Phys. Rev. Lett. 113, 160402 (2014).
[Crossref] [PubMed]

Rabelo, R.

R. Rabelo, M. Ho, D. Cavalcanti, N. Brunner, and V. Scarani, “Device-independent certification of entangled measurements,” Phys. Rev. Lett. 107, 050502 (2011).
[Crossref] [PubMed]

Rabl, P.

S. Kolkowitz, A. C. B. Jayich, Q. P. Unterreithmeier, S. D. Bennett, P. Rabl, J. G. E. Harris, and M. D. Lukin, “Coherent sensing of a mechanical resonator with a single-spin qubit,” Science 335, 1603–1606 (2012).
[Crossref] [PubMed]

Rangacharyulu, C.

H. Sakai, T. Saito, T. Ikeda, K. Itoh, T. Kawabata, H. Kuboki, Y. Maeda, N. Matsui, C. Rangacharyulu, M. Sasano, Y. Satou, K. Sekiguchi, K. Suda, A. Tamii, T. Uesaka, and K. Yako, “Spin correlations of strongly interacting massive fermion pairs as a test of Bell’s inequality,” Phys. Rev. Lett. 97, 150405 (2006).
[Crossref]

Reiserer, A.

B. Hensen, N. Kalb, M. S. Blok, A. E. Dréau, A. Reiserer, R. F. L. Vermeulen, R. N. Schouten, M. Markham, D. J. Twitchen, K. Goodenough, D. Elkouss, S. Wehner, T. H. Taminiau, and R. Hansona, “Loophole-free Bell test using electron spins in diamond: second experiment and additional analysis,” Sci. Rep. 6, 30289 (2016).
[Crossref] [PubMed]

B. Hensen, H. Bernien, A. E. Dréau, A. Reiserer, N. Kalb, M. S. Blok, J. Ruitenberg, R. F. L. Vermeulen, R. N. Schouten, C. Abellán, W. Amaya, V. Pruneri, M. W. Mitchell, M. Markham, D. J. Twitchen, D. Elkouss, S. Wehner, T. H. Taminiau, and R. Hanson, “Loophole-free Bell inequality violation using electron spins separated by 1.3 kilometres,” Nature 526, 682–686 (2015).
[Crossref] [PubMed]

Rowe, M. A.

M. A. Rowe, D. Kielpinski, V. Meyer, C. A. Sackett, W. M. Itano, C. Monroe, and D. J. Wineland, “Experimental violation of a Bell’s inequality with efficient detection,” Nature 409, 791–794 (2001).
[Crossref] [PubMed]

Roy, A.

A. Roy, S. S. Bhattacharya, A. Mukherjee, and M. Banik, “Optimal quantum violation of Clauser-Horne-Shimony-Holt like steering inequality,” J. Phys. A 48, 415302 (2015).
[Crossref]

Ruitenberg, J.

B. Hensen, H. Bernien, A. E. Dréau, A. Reiserer, N. Kalb, M. S. Blok, J. Ruitenberg, R. F. L. Vermeulen, R. N. Schouten, C. Abellán, W. Amaya, V. Pruneri, M. W. Mitchell, M. Markham, D. J. Twitchen, D. Elkouss, S. Wehner, T. H. Taminiau, and R. Hanson, “Loophole-free Bell inequality violation using electron spins separated by 1.3 kilometres,” Nature 526, 682–686 (2015).
[Crossref] [PubMed]

Sackett, C. A.

M. A. Rowe, D. Kielpinski, V. Meyer, C. A. Sackett, W. M. Itano, C. Monroe, and D. J. Wineland, “Experimental violation of a Bell’s inequality with efficient detection,” Nature 409, 791–794 (2001).
[Crossref] [PubMed]

Saito, T.

H. Sakai, T. Saito, T. Ikeda, K. Itoh, T. Kawabata, H. Kuboki, Y. Maeda, N. Matsui, C. Rangacharyulu, M. Sasano, Y. Satou, K. Sekiguchi, K. Suda, A. Tamii, T. Uesaka, and K. Yako, “Spin correlations of strongly interacting massive fermion pairs as a test of Bell’s inequality,” Phys. Rev. Lett. 97, 150405 (2006).
[Crossref]

Sakai, H.

H. Sakai, T. Saito, T. Ikeda, K. Itoh, T. Kawabata, H. Kuboki, Y. Maeda, N. Matsui, C. Rangacharyulu, M. Sasano, Y. Satou, K. Sekiguchi, K. Suda, A. Tamii, T. Uesaka, and K. Yako, “Spin correlations of strongly interacting massive fermion pairs as a test of Bell’s inequality,” Phys. Rev. Lett. 97, 150405 (2006).
[Crossref]

Sank, D.

M. Ansmann, H. Wang, R. C. Bialczak, M. Hofheinz, E. Lucero, M. Neeley, A. D. O’Connell, D. Sank, M. Weides, J. Wenner, A. N. Cleland, and J. M. Martinis, “Violation of Bell’s inequality in Josephson phase qubits,” Nature 461, 504–506 (2009).
[Crossref] [PubMed]

Sasano, M.

H. Sakai, T. Saito, T. Ikeda, K. Itoh, T. Kawabata, H. Kuboki, Y. Maeda, N. Matsui, C. Rangacharyulu, M. Sasano, Y. Satou, K. Sekiguchi, K. Suda, A. Tamii, T. Uesaka, and K. Yako, “Spin correlations of strongly interacting massive fermion pairs as a test of Bell’s inequality,” Phys. Rev. Lett. 97, 150405 (2006).
[Crossref]

Satou, Y.

H. Sakai, T. Saito, T. Ikeda, K. Itoh, T. Kawabata, H. Kuboki, Y. Maeda, N. Matsui, C. Rangacharyulu, M. Sasano, Y. Satou, K. Sekiguchi, K. Suda, A. Tamii, T. Uesaka, and K. Yako, “Spin correlations of strongly interacting massive fermion pairs as a test of Bell’s inequality,” Phys. Rev. Lett. 97, 150405 (2006).
[Crossref]

Scala, M.

M. Scala, M. S. Kim, G. W. Morley, P. F. Barker, and S. Bose, “Matter-wave interferometry of a levitated thermal nano-oscillator induced and probed by a spin,” Phys. Rev. Lett. 111, 180403 (2013).
[Crossref] [PubMed]

Scarani, V.

R. Rabelo, M. Ho, D. Cavalcanti, N. Brunner, and V. Scarani, “Device-independent certification of entangled measurements,” Phys. Rev. Lett. 107, 050502 (2011).
[Crossref] [PubMed]

M. Pawlowski, T. Paterek, D. Kaszlikowski, V. Scarani, A. Winter, and M. Zukowski, “Information causality as a physical principle,” Nature 461, 1101–1104 (2009).
[Crossref] [PubMed]

C. Branciard, N. Brunner, N. Gisin, C. Kurtsiefer, A. Lamas-Linares, A. Ling, and V. Scarani, “Testing quantum correlations versus single-particle properties within Leggett’s model and beyond,” Nat. Phys. 4, 681–685 (2008).
[Crossref]

C. Branciard, A. Ling, N. Gisin, C. Kurtsiefer, A. Lamas-Linares, and V. Scarani, “Experimental falsification of Leggett’s nonlocal variable model,” Phys. Rev. Lett. 99, 210407 (2007).
[Crossref]

Schouten, R. N.

B. Hensen, N. Kalb, M. S. Blok, A. E. Dréau, A. Reiserer, R. F. L. Vermeulen, R. N. Schouten, M. Markham, D. J. Twitchen, K. Goodenough, D. Elkouss, S. Wehner, T. H. Taminiau, and R. Hansona, “Loophole-free Bell test using electron spins in diamond: second experiment and additional analysis,” Sci. Rep. 6, 30289 (2016).
[Crossref] [PubMed]

B. Hensen, H. Bernien, A. E. Dréau, A. Reiserer, N. Kalb, M. S. Blok, J. Ruitenberg, R. F. L. Vermeulen, R. N. Schouten, C. Abellán, W. Amaya, V. Pruneri, M. W. Mitchell, M. Markham, D. J. Twitchen, D. Elkouss, S. Wehner, T. H. Taminiau, and R. Hanson, “Loophole-free Bell inequality violation using electron spins separated by 1.3 kilometres,” Nature 526, 682–686 (2015).
[Crossref] [PubMed]

Sekiguchi, K.

H. Sakai, T. Saito, T. Ikeda, K. Itoh, T. Kawabata, H. Kuboki, Y. Maeda, N. Matsui, C. Rangacharyulu, M. Sasano, Y. Satou, K. Sekiguchi, K. Suda, A. Tamii, T. Uesaka, and K. Yako, “Spin correlations of strongly interacting massive fermion pairs as a test of Bell’s inequality,” Phys. Rev. Lett. 97, 150405 (2006).
[Crossref]

Semenov, A. A.

M. O. Gumberidze, A. A. Semenov, D. Vasylyev, and W. Vogel, “Bell nonlocality in the turbulent atmosphere,” Phys. Rev. A 94, 053801 (2016).
[Crossref]

A. A. Semenov and W. Vogel, “Entanglement transfer through the turbulent atmosphere,” Phys. Rev. A 81, 023835 (2010).
[Crossref]

Sergienko, A. V.

P. G. Kwiat, K. Mattle, H. Weinfurter, A. Zeilinger, A. V. Sergienko, and Y. Shih, “New high-intensity source of polarization-entangled photon pairs,” Phy. Rev. Lett. 75, 4337 (1995).
[Crossref]

Sha, J.

X. Hao, C. L. Ma, and J. Sha, “Decoherence of quantum discord in an asymmetric-anisotropy spin system,” J. Phys. A: Math. Theor. 43, 425302 (2010).
[Crossref]

Shih, Y.

P. G. Kwiat, K. Mattle, H. Weinfurter, A. Zeilinger, A. V. Sergienko, and Y. Shih, “New high-intensity source of polarization-entangled photon pairs,” Phy. Rev. Lett. 75, 4337 (1995).
[Crossref]

Shimony, A.

J. F. Clauser, M. A. Horne, A. Shimony, and R. A. Holt, “Proposed experiment to test local hidden-variable theories,” Phys. Rev. Lett. 23, 880 (1969).
[Crossref]

Simon, C.

G. Weihs, T. Jennewein, C. Simon, H. Weinfurter, and A. Zeilinger, “Violation of Bell’s inequality under strict Einstein locality conditions,” Phys. Rev. Lett. 81, 5039 (1998).
[Crossref]

Song, L. J.

Z. Sun, X. M. Lu, and L. J. Song, “Quantum discord induced by a spin chain with quantum phase transition,” J. Phys. B: At. Mol. Opt. Phys. 43, 215504 (2010).
[Crossref]

Song, Z.

Z. Song, J.-Q. Liang, and L.-F. Wei, “Spin-Parity Effect in Violation of Bell’s Inequalities,” Mod. Phys. Lett. B 28, 1450004 (2014).
[Crossref]

Song, Z. G.

H. F. Zhang, J. H. Wang, Z. G. Song, J.-Q. Liang, and L.-F. Wei, “Spin-parity effect in violation of bell’s inequalities for entangled states of parallel polarization,” Mod. Phys. Lett. B 31, 1750032 (2017).
[Crossref]

Souza, S.

T. Werlang, S. Souza, F. F. Fanchini, and C. J. V. Boas, “Robustness of quantum discord to sudden death,” Phys. Rev. A 80, 024103 (2009).
[Crossref]

Stace, T. M.

T. M. Stace, G. J. Milburn, and C. H. W. Barnes, “Entangled two-photon source using biexciton emission of an asymmetric quantum dot in a cavity,” Phys. Rev. B 67, 085317 (2003).
[Crossref]

Strauch, F. W.

E. Polozova and F. W. Strauch, “Higher-dimensional Bell inequalities with noisy qudits,” Phys. Rev. A 93, 032130 (2016).
[Crossref]

Suda, K.

H. Sakai, T. Saito, T. Ikeda, K. Itoh, T. Kawabata, H. Kuboki, Y. Maeda, N. Matsui, C. Rangacharyulu, M. Sasano, Y. Satou, K. Sekiguchi, K. Suda, A. Tamii, T. Uesaka, and K. Yako, “Spin correlations of strongly interacting massive fermion pairs as a test of Bell’s inequality,” Phys. Rev. Lett. 97, 150405 (2006).
[Crossref]

Sun, F.-W.

X.-D. Chen, L.-M. Zhou, C.-L. Zou, C.-C. Li, Y. Dong, F.-W. Sun, and G.-C. Guo, “Spin depolarization effect induced by charge state conversion of nitrogen vacancy center in diamond,” Phys. Rev. B 92, 104301 (2015).
[Crossref]

Sun, Z.

Z. Sun, X. M. Lu, and L. J. Song, “Quantum discord induced by a spin chain with quantum phase transition,” J. Phys. B: At. Mol. Opt. Phys. 43, 215504 (2010).
[Crossref]

X. M. Lu, Z. Xi, Z. Sun, and X. Wang, “Geometric measure of quantum discord under decoherence,” Quantum Inf. Comput. 10, 994–1003 (2010).

Tamii, A.

H. Sakai, T. Saito, T. Ikeda, K. Itoh, T. Kawabata, H. Kuboki, Y. Maeda, N. Matsui, C. Rangacharyulu, M. Sasano, Y. Satou, K. Sekiguchi, K. Suda, A. Tamii, T. Uesaka, and K. Yako, “Spin correlations of strongly interacting massive fermion pairs as a test of Bell’s inequality,” Phys. Rev. Lett. 97, 150405 (2006).
[Crossref]

Taminiau, T. H.

B. Hensen, N. Kalb, M. S. Blok, A. E. Dréau, A. Reiserer, R. F. L. Vermeulen, R. N. Schouten, M. Markham, D. J. Twitchen, K. Goodenough, D. Elkouss, S. Wehner, T. H. Taminiau, and R. Hansona, “Loophole-free Bell test using electron spins in diamond: second experiment and additional analysis,” Sci. Rep. 6, 30289 (2016).
[Crossref] [PubMed]

B. Hensen, H. Bernien, A. E. Dréau, A. Reiserer, N. Kalb, M. S. Blok, J. Ruitenberg, R. F. L. Vermeulen, R. N. Schouten, C. Abellán, W. Amaya, V. Pruneri, M. W. Mitchell, M. Markham, D. J. Twitchen, D. Elkouss, S. Wehner, T. H. Taminiau, and R. Hanson, “Loophole-free Bell inequality violation using electron spins separated by 1.3 kilometres,” Nature 526, 682–686 (2015).
[Crossref] [PubMed]

Tittel, W.

W. Tittel, J. Brendel, B. Gisin, T. Herzog, H. Zbinden, and N. Gisin, “Experimental demonstration of quantum correlations over more than 10 km,” Phys. Rev. A 57, 3229 (1998).
[Crossref]

Twitchen, D. J.

B. Hensen, N. Kalb, M. S. Blok, A. E. Dréau, A. Reiserer, R. F. L. Vermeulen, R. N. Schouten, M. Markham, D. J. Twitchen, K. Goodenough, D. Elkouss, S. Wehner, T. H. Taminiau, and R. Hansona, “Loophole-free Bell test using electron spins in diamond: second experiment and additional analysis,” Sci. Rep. 6, 30289 (2016).
[Crossref] [PubMed]

B. Hensen, H. Bernien, A. E. Dréau, A. Reiserer, N. Kalb, M. S. Blok, J. Ruitenberg, R. F. L. Vermeulen, R. N. Schouten, C. Abellán, W. Amaya, V. Pruneri, M. W. Mitchell, M. Markham, D. J. Twitchen, D. Elkouss, S. Wehner, T. H. Taminiau, and R. Hanson, “Loophole-free Bell inequality violation using electron spins separated by 1.3 kilometres,” Nature 526, 682–686 (2015).
[Crossref] [PubMed]

Uesaka, T.

H. Sakai, T. Saito, T. Ikeda, K. Itoh, T. Kawabata, H. Kuboki, Y. Maeda, N. Matsui, C. Rangacharyulu, M. Sasano, Y. Satou, K. Sekiguchi, K. Suda, A. Tamii, T. Uesaka, and K. Yako, “Spin correlations of strongly interacting massive fermion pairs as a test of Bell’s inequality,” Phys. Rev. Lett. 97, 150405 (2006).
[Crossref]

Unterreithmeier, Q. P.

S. Kolkowitz, A. C. B. Jayich, Q. P. Unterreithmeier, S. D. Bennett, P. Rabl, J. G. E. Harris, and M. D. Lukin, “Coherent sensing of a mechanical resonator with a single-spin qubit,” Science 335, 1603–1606 (2012).
[Crossref] [PubMed]

Vasylyev, D.

M. O. Gumberidze, A. A. Semenov, D. Vasylyev, and W. Vogel, “Bell nonlocality in the turbulent atmosphere,” Phys. Rev. A 94, 053801 (2016).
[Crossref]

Vermeulen, R. F. L.

B. Hensen, N. Kalb, M. S. Blok, A. E. Dréau, A. Reiserer, R. F. L. Vermeulen, R. N. Schouten, M. Markham, D. J. Twitchen, K. Goodenough, D. Elkouss, S. Wehner, T. H. Taminiau, and R. Hansona, “Loophole-free Bell test using electron spins in diamond: second experiment and additional analysis,” Sci. Rep. 6, 30289 (2016).
[Crossref] [PubMed]

B. Hensen, H. Bernien, A. E. Dréau, A. Reiserer, N. Kalb, M. S. Blok, J. Ruitenberg, R. F. L. Vermeulen, R. N. Schouten, C. Abellán, W. Amaya, V. Pruneri, M. W. Mitchell, M. Markham, D. J. Twitchen, D. Elkouss, S. Wehner, T. H. Taminiau, and R. Hanson, “Loophole-free Bell inequality violation using electron spins separated by 1.3 kilometres,” Nature 526, 682–686 (2015).
[Crossref] [PubMed]

Vértesi, T.

M. T. Quintino, T. Vértesi, and N. Brunner, “Joint measurability, einstein-podolsky-rosen steering, and bell nonlocality,” Phys. Rev. Lett. 113, 160402 (2014).
[Crossref] [PubMed]

Vogel, W.

M. O. Gumberidze, A. A. Semenov, D. Vasylyev, and W. Vogel, “Bell nonlocality in the turbulent atmosphere,” Phys. Rev. A 94, 053801 (2016).
[Crossref]

A. A. Semenov and W. Vogel, “Entanglement transfer through the turbulent atmosphere,” Phys. Rev. A 81, 023835 (2010).
[Crossref]

Waldherr, G.

G. Waldherr, P. Neumann, S. F. Huelga, F. Jelezko, and J. Wrachtrup, “Violation of a temporal Bell inequality for single spins in a diamond defect center,” Phys. Rev. Lett. 107, 090401 (2011).
[Crossref] [PubMed]

Wan, J. T. K.

N. Zhao, J.-L. Hu, S.-W. Ho, J. T. K. Wan, and R. B. Liu, “Atomic-scale magnetometry of distant nuclear spin clusters via nitrogen-vacancy spin in diamond,” Nat. Nanotech. 6, 242–246 (2011).
[Crossref]

Wang, B.

B. Wang, Z. Y. Xu, Z. Q. Chen, and M. Feng, “Non-Markovian effect on the quantum discord,” Phys. Rev. A 81, 014101 (2010).
[Crossref]

Wang, H.

M. Ansmann, H. Wang, R. C. Bialczak, M. Hofheinz, E. Lucero, M. Neeley, A. D. O’Connell, D. Sank, M. Weides, J. Wenner, A. N. Cleland, and J. M. Martinis, “Violation of Bell’s inequality in Josephson phase qubits,” Nature 461, 504–506 (2009).
[Crossref] [PubMed]

Wang, J. H.

H. F. Zhang, J. H. Wang, Z. G. Song, J.-Q. Liang, and L.-F. Wei, “Spin-parity effect in violation of bell’s inequalities for entangled states of parallel polarization,” Mod. Phys. Lett. B 31, 1750032 (2017).
[Crossref]

Wang, M. H.

M. H. Wang, L. F. Wei, and J.-Q. Liang, “Does the Berry phase in a quantum optical system originate from the rotating wave approximation,” Phys. Lett. A 379, 1087–1090 (2015).
[Crossref]

Wang, X.

X. M. Lu, Z. Xi, Z. Sun, and X. Wang, “Geometric measure of quantum discord under decoherence,” Quantum Inf. Comput. 10, 994–1003 (2010).

Wang, Z. M.

Z. M. Wang, J. L. Lian, J.-Q. Liang, W-M Liu, and Y. M. Yu, “Collapse of the superradiant phase and multiple quantum phase transitions for Bose-Einstein condensates in an optomechanical cavity,” Phys. Rev. A 93, 033630 (2016).
[Crossref]

Wehner, S.

B. Hensen, N. Kalb, M. S. Blok, A. E. Dréau, A. Reiserer, R. F. L. Vermeulen, R. N. Schouten, M. Markham, D. J. Twitchen, K. Goodenough, D. Elkouss, S. Wehner, T. H. Taminiau, and R. Hansona, “Loophole-free Bell test using electron spins in diamond: second experiment and additional analysis,” Sci. Rep. 6, 30289 (2016).
[Crossref] [PubMed]

B. Hensen, H. Bernien, A. E. Dréau, A. Reiserer, N. Kalb, M. S. Blok, J. Ruitenberg, R. F. L. Vermeulen, R. N. Schouten, C. Abellán, W. Amaya, V. Pruneri, M. W. Mitchell, M. Markham, D. J. Twitchen, D. Elkouss, S. Wehner, T. H. Taminiau, and R. Hanson, “Loophole-free Bell inequality violation using electron spins separated by 1.3 kilometres,” Nature 526, 682–686 (2015).
[Crossref] [PubMed]

Wei, L. F.

M. H. Wang, L. F. Wei, and J.-Q. Liang, “Does the Berry phase in a quantum optical system originate from the rotating wave approximation,” Phys. Lett. A 379, 1087–1090 (2015).
[Crossref]

L. F. Wei, Y. X. Liu, and F. Nori, “Testing Bell’s inequality in a constantly coupled Josephson circuit by effective single-qubit operations,” Phys. Rev. B 72, 104516 (2005).
[Crossref]

Wei, L.-F.

H. F. Zhang, J. H. Wang, Z. G. Song, J.-Q. Liang, and L.-F. Wei, “Spin-parity effect in violation of bell’s inequalities for entangled states of parallel polarization,” Mod. Phys. Lett. B 31, 1750032 (2017).
[Crossref]

Z. Song, J.-Q. Liang, and L.-F. Wei, “Spin-Parity Effect in Violation of Bell’s Inequalities,” Mod. Phys. Lett. B 28, 1450004 (2014).
[Crossref]

Weides, M.

M. Ansmann, H. Wang, R. C. Bialczak, M. Hofheinz, E. Lucero, M. Neeley, A. D. O’Connell, D. Sank, M. Weides, J. Wenner, A. N. Cleland, and J. M. Martinis, “Violation of Bell’s inequality in Josephson phase qubits,” Nature 461, 504–506 (2009).
[Crossref] [PubMed]

Weihs, G.

G. Weihs, T. Jennewein, C. Simon, H. Weinfurter, and A. Zeilinger, “Violation of Bell’s inequality under strict Einstein locality conditions,” Phys. Rev. Lett. 81, 5039 (1998).
[Crossref]

Weinfurter, H.

G. Weihs, T. Jennewein, C. Simon, H. Weinfurter, and A. Zeilinger, “Violation of Bell’s inequality under strict Einstein locality conditions,” Phys. Rev. Lett. 81, 5039 (1998).
[Crossref]

P. G. Kwiat, K. Mattle, H. Weinfurter, A. Zeilinger, A. V. Sergienko, and Y. Shih, “New high-intensity source of polarization-entangled photon pairs,” Phy. Rev. Lett. 75, 4337 (1995).
[Crossref]

Wenner, J.

M. Ansmann, H. Wang, R. C. Bialczak, M. Hofheinz, E. Lucero, M. Neeley, A. D. O’Connell, D. Sank, M. Weides, J. Wenner, A. N. Cleland, and J. M. Martinis, “Violation of Bell’s inequality in Josephson phase qubits,” Nature 461, 504–506 (2009).
[Crossref] [PubMed]

Werlang, T.

T. Werlang, S. Souza, F. F. Fanchini, and C. J. V. Boas, “Robustness of quantum discord to sudden death,” Phys. Rev. A 80, 024103 (2009).
[Crossref]

Werner, R. F.

R. F. Werner, “Quantum states with Einstein-Podolsky-Rosen correlations admitting a hidden-variable model,” Phys. Rev. A 40, 4277 (1989).
[Crossref]

Wineland, D. J.

M. A. Rowe, D. Kielpinski, V. Meyer, C. A. Sackett, W. M. Itano, C. Monroe, and D. J. Wineland, “Experimental violation of a Bell’s inequality with efficient detection,” Nature 409, 791–794 (2001).
[Crossref] [PubMed]

Winter, A.

M. Pawlowski, T. Paterek, D. Kaszlikowski, V. Scarani, A. Winter, and M. Zukowski, “Information causality as a physical principle,” Nature 461, 1101–1104 (2009).
[Crossref] [PubMed]

Wootters, W. K.

W. K. Wootters, “Entanglement of formation of an arbitrary state of two qubits,” Phys. Rev. Lett. 80, 2245 (1998).
[Crossref]

Wrachtrup, J.

G. Waldherr, P. Neumann, S. F. Huelga, F. Jelezko, and J. Wrachtrup, “Violation of a temporal Bell inequality for single spins in a diamond defect center,” Phys. Rev. Lett. 107, 090401 (2011).
[Crossref] [PubMed]

Xi, Z.

X. M. Lu, Z. Xi, Z. Sun, and X. Wang, “Geometric measure of quantum discord under decoherence,” Quantum Inf. Comput. 10, 994–1003 (2010).

Xu, J. B.

S. B. Li and J. B. Xu, “Entanglement, Bell violation, and phase decoherence of two atoms inside an optical cavity,” Phys. Rev. A 72, 022332 (2005).
[Crossref]

Xu, J. S.

R. C. Ge, M. Gong, C. F. Li, J. S. Xu, and G. C. Guo, “Quantum correlation and classical correlation dynamics in the spin-boson model,” Phys. Rev. A 81, 064103 (2010).
[Crossref]

Xu, J.-B.

J.-B. Xu and S.-B. Li, “Control of the entanglement of two atoms in an optical cavity via white noise,” New J. Phys. 7, 72 (2005).
[Crossref]

Xu, Z. Y.

B. Wang, Z. Y. Xu, Z. Q. Chen, and M. Feng, “Non-Markovian effect on the quantum discord,” Phys. Rev. A 81, 014101 (2010).
[Crossref]

Yako, K.

H. Sakai, T. Saito, T. Ikeda, K. Itoh, T. Kawabata, H. Kuboki, Y. Maeda, N. Matsui, C. Rangacharyulu, M. Sasano, Y. Satou, K. Sekiguchi, K. Suda, A. Tamii, T. Uesaka, and K. Yako, “Spin correlations of strongly interacting massive fermion pairs as a test of Bell’s inequality,” Phys. Rev. Lett. 97, 150405 (2006).
[Crossref]

Yang, M.

X. L. Zhen, Q. Yang, M. Yang, and Z. L. Cao, “Bell-Nonlocality Dynamics of Three Remote Atoms in Tavis— Cummings and Jaynes—Cummings Models,” Commun. Theor. Phys. 62, 795–800 (2014).
[Crossref]

Yang, Q.

X. L. Zhen, Q. Yang, M. Yang, and Z. L. Cao, “Bell-Nonlocality Dynamics of Three Remote Atoms in Tavis— Cummings and Jaynes—Cummings Models,” Commun. Theor. Phys. 62, 795–800 (2014).
[Crossref]

Yin, Z.

M. Żukowski, A. Dutta, and Z. Yin, “Geometric Bell-like inequalities for steering,” Phys. Rev. A 91, 032107 (2015).
[Crossref]

N. Zhao and Z. Yin, “Room-temperature ultrasensitive mass spectrometer via dynamical decoupling,” Phys. Rev. A 90, 042118 (2014).
[Crossref]

Z. Yin, T. Li, X. Zhang, and L. M. Duan, “Large quantum superpositions of a levitated nanodiamond through spin-optomechanical coupling,” Phys. Rev. A 88, 033614 (2013).
[Crossref]

Yu, Y. M.

Z. M. Wang, J. L. Lian, J.-Q. Liang, W-M Liu, and Y. M. Yu, “Collapse of the superradiant phase and multiple quantum phase transitions for Bose-Einstein condensates in an optomechanical cavity,” Phys. Rev. A 93, 033630 (2016).
[Crossref]

Yuan, J. B.

J. B. Yuan, L. M. Kuang, and J. Q. Liao, “Amplification of quantum discord between two uncoupled qubits in a common environment by phase decoherence,” J. Phys. B: At. Mol. Opt. Phys. 43, 165503 (2010).
[Crossref]

Zbinden, H.

W. Tittel, J. Brendel, B. Gisin, T. Herzog, H. Zbinden, and N. Gisin, “Experimental demonstration of quantum correlations over more than 10 km,” Phys. Rev. A 57, 3229 (1998).
[Crossref]

Zeilinger, A.

S. Gröblacher, T. Paterek, R. Kaltenbaek, Č. Brukner, M. Żukowski, M. Aspelmeyer, and A. Zeilinger, “An experimental test of non-local realism,” Nature 446, 871–875 (2007).
[Crossref] [PubMed]

T. Paterek, A. Fedrizzi, S. Gröblacher, T. Jennewein, M. Żukowski, M. Aspelmeyer, and A. Zeilinger, “Experimental test of nonlocal realistic theories without the rotational symmetry assumption,” Phys. Rev. Lett. 99, 210406 (2007).
[Crossref]

G. Weihs, T. Jennewein, C. Simon, H. Weinfurter, and A. Zeilinger, “Violation of Bell’s inequality under strict Einstein locality conditions,” Phys. Rev. Lett. 81, 5039 (1998).
[Crossref]

P. G. Kwiat, K. Mattle, H. Weinfurter, A. Zeilinger, A. V. Sergienko, and Y. Shih, “New high-intensity source of polarization-entangled photon pairs,” Phy. Rev. Lett. 75, 4337 (1995).
[Crossref]

Zhang, H. F.

H. F. Zhang, J. H. Wang, Z. G. Song, J.-Q. Liang, and L.-F. Wei, “Spin-parity effect in violation of bell’s inequalities for entangled states of parallel polarization,” Mod. Phys. Lett. B 31, 1750032 (2017).
[Crossref]

Zhang, X.

Z. Yin, T. Li, X. Zhang, and L. M. Duan, “Large quantum superpositions of a levitated nanodiamond through spin-optomechanical coupling,” Phys. Rev. A 88, 033614 (2013).
[Crossref]

Zhang, Y.

Y. Zhang, S. Glancy, and E. Knill, “Asymptotically optimal data analysis for rejecting local realism,” Phy. Rev. A 84, 062118 (2011).
[Crossref]

Zhao, N.

N. Zhao and Z. Yin, “Room-temperature ultrasensitive mass spectrometer via dynamical decoupling,” Phys. Rev. A 90, 042118 (2014).
[Crossref]

N. Zhao, J.-L. Hu, S.-W. Ho, J. T. K. Wan, and R. B. Liu, “Atomic-scale magnetometry of distant nuclear spin clusters via nitrogen-vacancy spin in diamond,” Nat. Nanotech. 6, 242–246 (2011).
[Crossref]

Zhao, X. Q.

X. Q. Zhao, N. Liu, and J.-Q. Liang, “Nonlinear atom-photon-interaction-induced population inversion and inverted quantum phase transition of Bose-Einstein condensate in an optical cavity,” Phys. Rev. A 90, 023622 (2014).
[Crossref]

Zhen, X. L.

X. L. Zhen, Q. Yang, M. Yang, and Z. L. Cao, “Bell-Nonlocality Dynamics of Three Remote Atoms in Tavis— Cummings and Jaynes—Cummings Models,” Commun. Theor. Phys. 62, 795–800 (2014).
[Crossref]

Zhou, L.-M.

X.-D. Chen, L.-M. Zhou, C.-L. Zou, C.-C. Li, Y. Dong, F.-W. Sun, and G.-C. Guo, “Spin depolarization effect induced by charge state conversion of nitrogen vacancy center in diamond,” Phys. Rev. B 92, 104301 (2015).
[Crossref]

Zou, C.-L.

X.-D. Chen, L.-M. Zhou, C.-L. Zou, C.-C. Li, Y. Dong, F.-W. Sun, and G.-C. Guo, “Spin depolarization effect induced by charge state conversion of nitrogen vacancy center in diamond,” Phys. Rev. B 92, 104301 (2015).
[Crossref]

Zukowski, M.

M. Żukowski, A. Dutta, and Z. Yin, “Geometric Bell-like inequalities for steering,” Phys. Rev. A 91, 032107 (2015).
[Crossref]

M. Pawlowski, T. Paterek, D. Kaszlikowski, V. Scarani, A. Winter, and M. Zukowski, “Information causality as a physical principle,” Nature 461, 1101–1104 (2009).
[Crossref] [PubMed]

S. Gröblacher, T. Paterek, R. Kaltenbaek, Č. Brukner, M. Żukowski, M. Aspelmeyer, and A. Zeilinger, “An experimental test of non-local realism,” Nature 446, 871–875 (2007).
[Crossref] [PubMed]

T. Paterek, A. Fedrizzi, S. Gröblacher, T. Jennewein, M. Żukowski, M. Aspelmeyer, and A. Zeilinger, “Experimental test of nonlocal realistic theories without the rotational symmetry assumption,” Phys. Rev. Lett. 99, 210406 (2007).
[Crossref]

Commun. Theor. Phys. (1)

X. L. Zhen, Q. Yang, M. Yang, and Z. L. Cao, “Bell-Nonlocality Dynamics of Three Remote Atoms in Tavis— Cummings and Jaynes—Cummings Models,” Commun. Theor. Phys. 62, 795–800 (2014).
[Crossref]

Found. Phys. (1)

A. J. Leggett, “Nonlocal hidden-variable theories and quantum mechanics: An incompatibility theorem,” Found. Phys. 33, 1469–1493 (2003).
[Crossref]

J. Phys. A (2)

A. Roy, S. S. Bhattacharya, A. Mukherjee, and M. Banik, “Optimal quantum violation of Clauser-Horne-Shimony-Holt like steering inequality,” J. Phys. A 48, 415302 (2015).
[Crossref]

P. Bierhorst, “A robust mathematical model for a loophole-free Clauser–Horne experiment,” J. Phys. A 48, 195302 (2015).
[Crossref]

J. Phys. A: Math. Theor. (2)

F. Altintas and R. J. Eryigit, “Dynamics of entanglement and Bell non-locality for two stochastic qubits with dipole–dipole interaction,” J. Phys. A: Math. Theor. 43, 415306 (2010).
[Crossref]

X. Hao, C. L. Ma, and J. Sha, “Decoherence of quantum discord in an asymmetric-anisotropy spin system,” J. Phys. A: Math. Theor. 43, 425302 (2010).
[Crossref]

J. Phys. B: At. Mol. Opt. Phys. (2)

J. B. Yuan, L. M. Kuang, and J. Q. Liao, “Amplification of quantum discord between two uncoupled qubits in a common environment by phase decoherence,” J. Phys. B: At. Mol. Opt. Phys. 43, 165503 (2010).
[Crossref]

Z. Sun, X. M. Lu, and L. J. Song, “Quantum discord induced by a spin chain with quantum phase transition,” J. Phys. B: At. Mol. Opt. Phys. 43, 215504 (2010).
[Crossref]

Mod. Phys. Lett. B (2)

H. F. Zhang, J. H. Wang, Z. G. Song, J.-Q. Liang, and L.-F. Wei, “Spin-parity effect in violation of bell’s inequalities for entangled states of parallel polarization,” Mod. Phys. Lett. B 31, 1750032 (2017).
[Crossref]

Z. Song, J.-Q. Liang, and L.-F. Wei, “Spin-Parity Effect in Violation of Bell’s Inequalities,” Mod. Phys. Lett. B 28, 1450004 (2014).
[Crossref]

Nat. Nanotech. (1)

N. Zhao, J.-L. Hu, S.-W. Ho, J. T. K. Wan, and R. B. Liu, “Atomic-scale magnetometry of distant nuclear spin clusters via nitrogen-vacancy spin in diamond,” Nat. Nanotech. 6, 242–246 (2011).
[Crossref]

Nat. Phys. (2)

A. C. Dada, J. Leach, G. S. Buller, M. J. Padgett, and E. Andersson, “Experimental high-dimensional two-photon entanglement and violations of generalized Bell inequalities,” Nat. Phys. 7, 677–680 (2011).
[Crossref]

C. Branciard, N. Brunner, N. Gisin, C. Kurtsiefer, A. Lamas-Linares, A. Ling, and V. Scarani, “Testing quantum correlations versus single-particle properties within Leggett’s model and beyond,” Nat. Phys. 4, 681–685 (2008).
[Crossref]

Nature (7)

S. Gröblacher, T. Paterek, R. Kaltenbaek, Č. Brukner, M. Żukowski, M. Aspelmeyer, and A. Zeilinger, “An experimental test of non-local realism,” Nature 446, 871–875 (2007).
[Crossref] [PubMed]

S. Pironio, A. Acín, S. Massar, A. Boyer de lai Giroday, D. N. Matsukevich, P. Maunz, S. Olmschenk, D. Hayes, L. Luo, T. A. Manning, and C. Monroe, “Random numbers certified by Bell’s theorem,” Nature 464, 1021–1024 (2010).
[Crossref] [PubMed]

M. Pawlowski, T. Paterek, D. Kaszlikowski, V. Scarani, A. Winter, and M. Zukowski, “Information causality as a physical principle,” Nature 461, 1101–1104 (2009).
[Crossref] [PubMed]

A. Aspect, “Violation of Bell’s inequality under strict Einstein locality conditions,” Nature 398, 189–190 (1999).
[Crossref]

M. A. Rowe, D. Kielpinski, V. Meyer, C. A. Sackett, W. M. Itano, C. Monroe, and D. J. Wineland, “Experimental violation of a Bell’s inequality with efficient detection,” Nature 409, 791–794 (2001).
[Crossref] [PubMed]

B. Hensen, H. Bernien, A. E. Dréau, A. Reiserer, N. Kalb, M. S. Blok, J. Ruitenberg, R. F. L. Vermeulen, R. N. Schouten, C. Abellán, W. Amaya, V. Pruneri, M. W. Mitchell, M. Markham, D. J. Twitchen, D. Elkouss, S. Wehner, T. H. Taminiau, and R. Hanson, “Loophole-free Bell inequality violation using electron spins separated by 1.3 kilometres,” Nature 526, 682–686 (2015).
[Crossref] [PubMed]

M. Ansmann, H. Wang, R. C. Bialczak, M. Hofheinz, E. Lucero, M. Neeley, A. D. O’Connell, D. Sank, M. Weides, J. Wenner, A. N. Cleland, and J. M. Martinis, “Violation of Bell’s inequality in Josephson phase qubits,” Nature 461, 504–506 (2009).
[Crossref] [PubMed]

New J. Phys. (1)

J.-B. Xu and S.-B. Li, “Control of the entanglement of two atoms in an optical cavity via white noise,” New J. Phys. 7, 72 (2005).
[Crossref]

Opt. Commun. (1)

R. X. Chen, C. Hu, and L. Miao, “Dynamics of Bell-nonlocality of two-mode squeezed vacuum fields interacting with atoms,” Opt. Commun. 284, 2955–2959 (2011).
[Crossref]

Phy. Rev. A (1)

Y. Zhang, S. Glancy, and E. Knill, “Asymptotically optimal data analysis for rejecting local realism,” Phy. Rev. A 84, 062118 (2011).
[Crossref]

Phy. Rev. Lett. (1)

P. G. Kwiat, K. Mattle, H. Weinfurter, A. Zeilinger, A. V. Sergienko, and Y. Shih, “New high-intensity source of polarization-entangled photon pairs,” Phy. Rev. Lett. 75, 4337 (1995).
[Crossref]

Phys. Lett. A (6)

J. Q. Li and J. Q. Liang, “Disentanglement and Bell nonlocality in a classical dephasing environment,” Phys. Lett. A 374, 1975–1979 (2010).
[Crossref]

F. Altintas and R. Eryigit, “Quantum correlations in non-Markovian environments,” Phys. Lett. A 374, 4283 (2010).
[Crossref]

R. Horodecki, P. Horodecki, and M. Horodecki, “Violating Bell inequality by mixed spin-12 states: necessary and sufficient condition,” Phys. Lett. A 200, 340–344 (1995).
[Crossref]

R. Horodecki, “Two-spin-12 mixtures and Bell’s inequalities,” Phys. Lett. A 210, 223–226 (1996).
[Crossref]

M. H. Wang, L. F. Wei, and J.-Q. Liang, “Does the Berry phase in a quantum optical system originate from the rotating wave approximation,” Phys. Lett. A 379, 1087–1090 (2015).
[Crossref]

N. Gisin, “Bell’s inequality holds for all non-product states,” Phys. Lett. A 154, 201–202 (1991).
[Crossref]

Phys. Rev. A (24)

X. Q. Zhao, N. Liu, and J.-Q. Liang, “Nonlinear atom-photon-interaction-induced population inversion and inverted quantum phase transition of Bose-Einstein condensate in an optical cavity,” Phys. Rev. A 90, 023622 (2014).
[Crossref]

Z. M. Wang, J. L. Lian, J.-Q. Liang, W-M Liu, and Y. M. Yu, “Collapse of the superradiant phase and multiple quantum phase transitions for Bose-Einstein condensates in an optomechanical cavity,” Phys. Rev. A 93, 033630 (2016).
[Crossref]

M. S. Kim, J. Lee, D. Ahn, and P. L. Knight, “Entanglement induced by a single-mode heat environment,” Phys. Rev. A 65, 040101 (2002).
[Crossref]

T. Werlang, S. Souza, F. F. Fanchini, and C. J. V. Boas, “Robustness of quantum discord to sudden death,” Phys. Rev. A 80, 024103 (2009).
[Crossref]

E. Polozova and F. W. Strauch, “Higher-dimensional Bell inequalities with noisy qudits,” Phys. Rev. A 93, 032130 (2016).
[Crossref]

N. Zhao and Z. Yin, “Room-temperature ultrasensitive mass spectrometer via dynamical decoupling,” Phys. Rev. A 90, 042118 (2014).
[Crossref]

Z. Yin, T. Li, X. Zhang, and L. M. Duan, “Large quantum superpositions of a levitated nanodiamond through spin-optomechanical coupling,” Phys. Rev. A 88, 033614 (2013).
[Crossref]

S. B. Li and J. B. Xu, “Entanglement, Bell violation, and phase decoherence of two atoms inside an optical cavity,” Phys. Rev. A 72, 022332 (2005).
[Crossref]

B. Wang, Z. Y. Xu, Z. Q. Chen, and M. Feng, “Non-Markovian effect on the quantum discord,” Phys. Rev. A 81, 014101 (2010).
[Crossref]

R. C. Ge, M. Gong, C. F. Li, J. S. Xu, and G. C. Guo, “Quantum correlation and classical correlation dynamics in the spin-boson model,” Phys. Rev. A 81, 064103 (2010).
[Crossref]

F. Francica, F. Plastina, and S. Maniscalco, “Quantum Zeno and anti-Zeno effects on quantum and classical correlations,” Phys. Rev. A 82, 052118 (2010).
[Crossref]

J. Barrett, D. Collins, L. Hardy, A. Kent, and S. Popescu, “Quantum nonlocality, Bell inequalities, and the memory loophole,” Phys. Rev. A 66, 042111 (2002).
[Crossref]

M. Żukowski, A. Dutta, and Z. Yin, “Geometric Bell-like inequalities for steering,” Phys. Rev. A 91, 032107 (2015).
[Crossref]

P. Pandya, A. Misra, and I. Chakrabarty, “Complementarity between tripartite quantum correlation and bipartite Bell-inequality violation in three-qubit states,” Phys. Rev. A 94, 052126 (2016).
[Crossref]

A. A. Semenov and W. Vogel, “Entanglement transfer through the turbulent atmosphere,” Phys. Rev. A 81, 023835 (2010).
[Crossref]

M. O. Gumberidze, A. A. Semenov, D. Vasylyev, and W. Vogel, “Bell nonlocality in the turbulent atmosphere,” Phys. Rev. A 94, 053801 (2016).
[Crossref]

L. Mazzola, B. Bellomo, R. L. Franco, and G. Compagno, “Bell nonlocality in the turbulent atmosphere,” Phys. Rev. A 81, 052116 (2010).
[Crossref]

A. G. Kofman and A. N. Korotkov, “Bell-inequality violation versus entanglement in the presence of local decoherence,” Phys. Rev. A 77, 052329 (2008).
[Crossref]

Ł. Derkacz and L. Jakobczyk, “Clauser-Horne-Shimony-Holt violation and the entropy-concurrence plane,” Phys. Rev. A 72, 042321 (2005).
[Crossref]

R. F. Werner, “Quantum states with Einstein-Podolsky-Rosen correlations admitting a hidden-variable model,” Phys. Rev. A 40, 4277 (1989).
[Crossref]

W. Tittel, J. Brendel, B. Gisin, T. Herzog, H. Zbinden, and N. Gisin, “Experimental demonstration of quantum correlations over more than 10 km,” Phys. Rev. A 57, 3229 (1998).
[Crossref]

M. D. Eisaman, E. A. Goldschmidt, J. Chen, J. Fan, and A. Migdall, “Experimental test of nonlocal realism using a fiber-based source of polarization-entangled photon pairs,” Phys. Rev. A 77, 032339 (2008).
[Crossref]

M. Paternostro and H. Jeong, “Testing nonlocal realism with entangled coherent states,” Phys. Rev. A 81, 032115 (2010).
[Crossref]

C.-W. Lee, M. Paternostro, and H. Jeong, “Faithful test of nonlocal realism with entangled coherent states,” Phys. Rev. A 83, 022102 (2011).
[Crossref]

Phys. Rev. B (3)

L. F. Wei, Y. X. Liu, and F. Nori, “Testing Bell’s inequality in a constantly coupled Josephson circuit by effective single-qubit operations,” Phys. Rev. B 72, 104516 (2005).
[Crossref]

T. M. Stace, G. J. Milburn, and C. H. W. Barnes, “Entangled two-photon source using biexciton emission of an asymmetric quantum dot in a cavity,” Phys. Rev. B 67, 085317 (2003).
[Crossref]

X.-D. Chen, L.-M. Zhou, C.-L. Zou, C.-C. Li, Y. Dong, F.-W. Sun, and G.-C. Guo, “Spin depolarization effect induced by charge state conversion of nitrogen vacancy center in diamond,” Phys. Rev. B 92, 104301 (2015).
[Crossref]

Phys. Rev. Lett. (10)

M. Scala, M. S. Kim, G. W. Morley, P. F. Barker, and S. Bose, “Matter-wave interferometry of a levitated thermal nano-oscillator induced and probed by a spin,” Phys. Rev. Lett. 111, 180403 (2013).
[Crossref] [PubMed]

G. Waldherr, P. Neumann, S. F. Huelga, F. Jelezko, and J. Wrachtrup, “Violation of a temporal Bell inequality for single spins in a diamond defect center,” Phys. Rev. Lett. 107, 090401 (2011).
[Crossref] [PubMed]

W. K. Wootters, “Entanglement of formation of an arbitrary state of two qubits,” Phys. Rev. Lett. 80, 2245 (1998).
[Crossref]

H. Sakai, T. Saito, T. Ikeda, K. Itoh, T. Kawabata, H. Kuboki, Y. Maeda, N. Matsui, C. Rangacharyulu, M. Sasano, Y. Satou, K. Sekiguchi, K. Suda, A. Tamii, T. Uesaka, and K. Yako, “Spin correlations of strongly interacting massive fermion pairs as a test of Bell’s inequality,” Phys. Rev. Lett. 97, 150405 (2006).
[Crossref]

G. Weihs, T. Jennewein, C. Simon, H. Weinfurter, and A. Zeilinger, “Violation of Bell’s inequality under strict Einstein locality conditions,” Phys. Rev. Lett. 81, 5039 (1998).
[Crossref]

C. Branciard, A. Ling, N. Gisin, C. Kurtsiefer, A. Lamas-Linares, and V. Scarani, “Experimental falsification of Leggett’s nonlocal variable model,” Phys. Rev. Lett. 99, 210407 (2007).
[Crossref]

R. Rabelo, M. Ho, D. Cavalcanti, N. Brunner, and V. Scarani, “Device-independent certification of entangled measurements,” Phys. Rev. Lett. 107, 050502 (2011).
[Crossref] [PubMed]

T. Paterek, A. Fedrizzi, S. Gröblacher, T. Jennewein, M. Żukowski, M. Aspelmeyer, and A. Zeilinger, “Experimental test of nonlocal realistic theories without the rotational symmetry assumption,” Phys. Rev. Lett. 99, 210406 (2007).
[Crossref]

J. F. Clauser, M. A. Horne, A. Shimony, and R. A. Holt, “Proposed experiment to test local hidden-variable theories,” Phys. Rev. Lett. 23, 880 (1969).
[Crossref]

M. T. Quintino, T. Vértesi, and N. Brunner, “Joint measurability, einstein-podolsky-rosen steering, and bell nonlocality,” Phys. Rev. Lett. 113, 160402 (2014).
[Crossref] [PubMed]

Quantum Inf. Comput. (1)

X. M. Lu, Z. Xi, Z. Sun, and X. Wang, “Geometric measure of quantum discord under decoherence,” Quantum Inf. Comput. 10, 994–1003 (2010).

Sci. Rep. (1)

B. Hensen, N. Kalb, M. S. Blok, A. E. Dréau, A. Reiserer, R. F. L. Vermeulen, R. N. Schouten, M. Markham, D. J. Twitchen, K. Goodenough, D. Elkouss, S. Wehner, T. H. Taminiau, and R. Hansona, “Loophole-free Bell test using electron spins in diamond: second experiment and additional analysis,” Sci. Rep. 6, 30289 (2016).
[Crossref] [PubMed]

Science (1)

S. Kolkowitz, A. C. B. Jayich, Q. P. Unterreithmeier, S. D. Bennett, P. Rabl, J. G. E. Harris, and M. D. Lukin, “Coherent sensing of a mechanical resonator with a single-spin qubit,” Science 335, 1603–1606 (2012).
[Crossref] [PubMed]

Other (2)

G. Jaeger, Entanglement, Information, and the Interpretation of Quantum Mechanics (Springer, 2010).

M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information (Cambridge University Press, 2000).

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (4)

Fig. 1
Fig. 1 The maximum quantum CHSH-probability P CHSH max ( t ) (a) and concurrence C(t) (b) as functions of time t measured in the period T of optic field for the entangled-state of antiparallel spin-polarization with angle parameters η = 0 and ξ = π/6 (green solid line), π/4 (blue dot and dash line) π/3 (red dash line) with average photon-number γ2 = 0.01 (1), 1 (2), 15 (3), 150 (4). P CHSH max ( t ) = 2 2 , C(t) = 1 not varying with time for the spin singlet state |Ψ1〉.
Fig. 2
Fig. 2 Time-variation curves of P CHSH max ( t ) (a) and C(t) (b) for the entangled-state of antiparallel spin-polarization with angle parameters ξ = π/4 and η = π/6 (green solid line), π/4 (blue dot and dash line) π/3 (pink dash line) with average photon-number γ2 = 0.01 (1), 1 (2), 15 (3), 150 (4).
Fig. 3
Fig. 3 The maximum CHSH correlation-probability P CHSH max ( t ) (upper panel) concurrence C(t) (lower panel) as functions of time t in the initial entangled states of parallel spin-polarizations with angle parameters η = 0, ξ = π/3, π/4, and 3π/4 for the average photon-number γ2 = 0.01 (1), 1 (2), 15 (3), 150 (4).
Fig. 4
Fig. 4 The time variation of P CHSH max ( t ) (upper panel) and concurrence C(t) (lower panel) in the entangled states of parallel spin-polarizations with the angle parameters ξ = π/4, η = π/6, π/4, and π/3 for the average photon-number γ2 = 0.01 (1), 1 (2), 15 (3), 150 (4).

Equations (68)

Equations on this page are rendered with MathJax. Learn more.

H = ω q a + i g i = 1 2 ( a σ i + a σ i ) ,
H sp ( α ) = α | H | α = ω γ 2 + i = 1 2 i γ g [ e i ϕ σ i + e i ϕ σ i ] .
ε 0 ( γ ) = ω γ 2 2 g γ , ε 3 ( γ ) = ω γ 2 + 2 g γ , ε 1 ( γ ) = ε 2 ( γ ) = ω γ 2 ,
| ψ 0 = 1 2 [ e i ϕ | , e i ϕ | + , + i ( | + , + | , + ) ] , | ψ 3 = 1 2 [ e i ϕ | , e i ϕ | + , + i ( | + , + | , + ) ] , | ψ 2 = 1 2 ( e i ϕ | + , + e i ϕ | , ) , | ψ 1 = 1 2 ( | , + | + , ) ,
| ψ = sin ξ e i η | + , + cos ξ e i η | , + ,
ρ ψ = ρ ψ lc + ρ ψ nlc .
ρ ψ lc = sin 2 ξ | + , + , | + cos 2 ξ | , + , + | ,
ρ ψ nlc = sin ξ cos ξ e 2 η | + , , + | + sin ξ cos ξ e i 2 η | , + + , | ,
σ a | ± a = ± | ± a
σ b | ± b = ± | ± b ,
| + n = cos ( θ n 2 ) | + + sin ( θ n 2 ) e Φ n |
| + n = sin ( θ n 2 ) | + + cos ( θ n 2 ) e Φ n | ,
| 1 = | + a , + b , | 2 = | + a , b , | 3 = | a , + b , | 4 = | a , b .
P ( a , b ) = T r [ ( σ a ) ( σ b ) ρ ψ ] .
P ( a , b ) = P lc ( a , b ) + P nlc ( a , b ) .
P lc ( a , b ) = cos θ a cos θ b .
P CHSH = | P ( a , b ) + P ( a , c ) + P ( d , b ) P ( d , c ) | ,
P CHSH lc = | cos θ a ( cos θ b + cos θ c ) + cos θ d ( cos θ b cos θ c | 2 ,
P ( a , b ) = a b ,
P CHSH = | a ( b + c ) + d ( b c ) | .
P CHSH max = 2 2 ,
| ψ = sin ξ e i η | + , + + cos ξ e i η | , ,
P lc ( a , b ) = cos θ a cos θ b ,
R ( t ) = e i ω a a t .
H i = R ( t ) H R ( t ) i R ( t ) t R ( t ) = i f i = 1 2 ( a e ω t σ i + a e i ω t σ i ) .
U ( t ) = R ( t ) U i ( t ) ,
U i ( t ) = ( 1 2 a sin 2 ( g t S 2 ) S a a sin ( g t 2 S ) 2 S a sin ( g t 2 S ) 2 S 2 a sin 2 ( g t S 2 ) S a sin ( g t 2 S ) 2 S a cos 2 ( g t S 2 ) sin 2 ( g t S 2 ) sin ( g t 2 S ) 2 S a sin ( g t 2 S ) 2 S a sin 2 ( g t S 2 ) cos 2 ( g t S 2 ) sin ( g t 2 S ) 2 S a 2 a sin 2 ( g t S 2 ) S a a sin ( g t 2 S ) 2 S a sin ( g t 2 S ) 2 S 1 2 a sin 2 ( g t S 2 ) S a )
i d ρ ( t ) d t = [ H , ρ ( t ) ] ,
ρ ( 0 ) = ρ ψ ( 0 ) ρ f ( 0 ) ,
ρ ψ ( 0 ) = ( 0 0 0 0 0 sin 2 ξ sin ξ cos ξ e i 2 η 0 0 sin ξ cos ξ e i 2 η cos 2 ξ 0 0 0 0 0 ) .
ρ r ( t ) = n = 0 ρ n ( t ) , ρ n ( t ) = n | ρ ( t ) | n ,
ρ n ( t ) = j , i = 0 n | U ( t ) | j ρ ψ ( 0 ) l | U ( t ) | n γ j + l e i ( j l ) ϕ j ! l ! e γ 2 .
ρ r ( t ) = n = 0 ( ( ρ n ) 11 ( ρ n ) 12 ( ρ n ) 13 ( ρ n ) 14 ( ρ n * ) 12 ( ρ n ) 22 ( ρ n ) 23 ( ρ n ) 24 ( ρ n * ) 13 ( ρ n * ) 23 ( ρ n ) 33 ( ρ n ) 34 ( ρ n * ) 14 ( ρ n * ) 24 ( ρ n * ) 34 ( ρ n ) 44 ) .
( ρ n ) 11 = e 1 | ρ n | e 1 = e γ 2 n ! C 1 2 ( sin 2 ξ cos 2 η + 1 ) ,
( ρ n ) 22 = e γ 2 n ! ( C 2 2 sin 2 ξ + C 3 2 cos 2 ξ + C 2 C 3 sin 2 ξ cos 2 η ) ,
( ρ n ) 33 = e γ 2 n ! ( C 2 2 cos 2 ξ + C 3 2 sin 2 ξ + C 2 C 3 sin 2 ξ cos 2 η ) ,
( ρ n ) 44 = e γ 2 n ! C 4 2 ( sin 2 ξ cos 2 η + 1 ) ,
( ρ n ) 12 = e γ 2 n ! C 1 e 2 i η ( C 2 sin ξ + C 3 e 2 i η cos ξ ) ( e 2 i η sin ξ + cos ξ ) ,
( ρ n ) 13 = e γ 2 n ! C 1 e 2 i η ( C 2 e 2 i η cos ξ + C 3 sin ξ ) ( e 2 i η sin ξ + cos ξ ) ,
( ρ n ) 14 = e γ 2 n ! C 1 C 4 ( sin 2 ξ cos 2 η + 1 ) ,
( ρ n ) 23 = e γ 2 n ! ( C 2 2 e 2 i η sin 2 ξ + 2 C 2 C 3 + C 3 2 e 2 i η sin 2 ξ ) ,
( ρ n ) 24 = e γ 2 n ! C 4 e 2 i η ( C 2 e 2 i η sin ξ + C 3 cos ξ ) ( e 2 i η cos ξ + sin ξ ) ,
( ρ n ) 34 = e γ 2 n ! C 4 e 2 i η ( C 2 cos ξ + C 3 e 2 i η sin ξ ) ( e 2 i η cos ξ + sin ξ ) .
C 1 = γ n + 1 sin ( g t 4 n + 6 ) 4 n + 6 ,
C 2 = γ n cos 2 ( g t 2 n + 1 2 ) ,
C 3 = γ n sin 2 ( g t 2 n + 1 2 ) ,
C 4 = γ n 1 n sin ( g t 4 n 2 ) 4 n 2 .
ρ ψ ( 0 ) = ( sin 2 ξ 0 0 sin ξ cos ξ e 2 i η 0 0 0 0 0 0 0 0 sin ξ cos ξ e 2 i η 0 0 cos 2 ξ ) .
( ρ n ) 11 = e γ 2 n ! ( D 1 2 sin 2 ξ + D 2 2 cos 2 ξ + D 1 D 2 sin 2 ξ cos 2 η ) ,
( ρ n ) 22 = e γ 2 n ! ( D 3 2 sin 2 ξ + D 4 2 cos 2 ξ + D 3 D 4 sin 2 ξ cos 2 η ) ,
( ρ n ) 44 = e γ 2 n ! ( D 5 2 sin 2 ξ + D 6 2 cos 2 ξ + D 5 D 6 sin 2 ξ cos 2 η ) ,
( ρ n ) 33 = ( ρ n ) 22 ,
( ρ n ) 12 = e γ 2 n ! ( D 4 cos ξ + e 2 i η D 3 sin ξ ) ( D 2 cos ξ + e 2 i η D 1 sin ξ ) ,
( ρ n ) 14 = e γ 2 n ! ( D 6 cos ξ + e 2 i η D 5 sin ξ ) ( D 2 cos ξ + e 2 i η D 1 sin ξ ) ,
( ρ n ) 24 = e γ 2 n ! ( D 6 cos ξ + e 2 i η D 5 sin ξ ) ( D 4 cos ξ + e 2 i η D 3 sin ξ ) ,
( ρ n ) 13 = ( ρ n ) 12 ,
( ρ n ) 23 = ( ρ n ) 22 ,
( ρ n ) 34 = ( ρ n ) 24 ,
D 1 = γ n ( 1 2 ( n + 1 ) sin 2 ( g t 2 n + 3 2 ) 2 n + 3 ) ,
D 2 = γ n + 2 2 sin 2 ( g t 2 n + 3 2 ) 2 n + 3 ,
D 3 = γ n 1 n sin ( g t 4 n + 2 ) 4 n + 2 ,
D 4 = γ n + 1 sin ( g t 4 n + 2 ) 4 n + 2 ,
D 5 = γ n 2 2 n ( n 1 ) sin 2 ( g t 2 n 1 2 ) 2 n 1 ,
D 6 = γ n ( 1 2 n sin 2 ( g t 2 n 1 2 ) 2 n 1 ) .
T ρ r ( t ) = ρ r ( t ) σ σ .
U ρ ( r ) = T ρ r ( t ) T T ρ r ( t ) ,
P CHSH max ( t ) = 2 m ( ρ r ) .
C ( t ) = max { 0 , Λ ( t ) } ,

Metrics