Abstract

We propose a construction scheme of a two-photon polarization controlled arbitrary phase gate based on weak cross-phase modulation. Assisted with weak cross-phase modulation and homodyne measurement on the coherent states, the individual photons are entangled together. Employing the combination of optical elements and classical feed-forward techniques, the target photon can have a conditionally shifted arbitrary phase with efficiency approaching nearly unity. With a large-amplitude coherent state, the high success probability of the controlled arbitrary phase gate can be guaranteed.

© 2013 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information (Cambridge University, 2000).
  2. K. S. Choi, H. Deng, J. Laurat, and H. J. Kimble, “Mapping photonic entanglement into and out of a quantum memory,” Nature 452, 67–71 (2008).
    [CrossRef]
  3. M. Mariantoni, H. Wang, T. Yamamoto, M. Neeley, R. C. Bialczak, Y. Chen, M. Lenander, E. Lucero, A. D. OConnell, D. Sank, M. Weides, J. Wenner, Y. Yin, J. Zhao, A. N. Korotkov, A. N. Cleland, and J. M. Martinis, “Implementing the quantum von Neumann architecture with superconducting circuits,” Science 334, 61–65 (2011).
    [CrossRef]
  4. A. Barenco, D. Deutsch, A. Ekert, and R. Jozsa, “Conditional quantum dynamics and logic gates,” Phys. Rev. Lett. 74, 4083–4086 (1995).
    [CrossRef]
  5. J. Cirac and P. Zoller, “Quantum computations with cold trapped ions,” Phys. Rev. Lett. 74, 4091–4094 (1995).
    [CrossRef]
  6. I. Chuang and Y. Yamamoto, “Simple quantum computer,” Phys. Rev. A 52, 3489–3496 (1995).
    [CrossRef]
  7. A. Sørensen and K. Mølmer, “Quantum computation with ions in thermal motion,” Phys. Rev. Lett. 82, 1971–1974 (1999).
    [CrossRef]
  8. M. Koashi, T. Yamamoto, and N. Imoto, “Probabilistic manipulation of entangled photons,” Phys. Rev. A 63, 030301(R) (2001).
    [CrossRef]
  9. T. Pittman, B. Jacobs, and J. Franson, “Probabilistic quantum logic operations using polarizing beam splitters,” Phys. Rev. A 64, 062311 (2001).
    [CrossRef]
  10. F. Schmidt-Kaler, H. Häffner, M. Riebe, S. Gulde, G. P. T. Lancaster, T. Deuschle, C. Becher, C. F. Roos, J. Eschner, and R. Blatt, “Realization of the Cirac–Zoller controlled-NOT quantum gate,” Nature 422, 408–411 (2003).
    [CrossRef]
  11. Q. A. Turchette, C. J. Hood, W. Lange, H. Mabuchi, and H. J. Kimble, “Measurement of conditional phase shifts for quantum logic,” Phys. Rev. Lett. 75, 4710–4713 (1995).
    [CrossRef]
  12. L. You, X. X. Yi, and X. H. Su, “Quantum logic between atoms inside a high-Q optical cavity,” Phys. Rev. A 67, 032308 (2003).
    [CrossRef]
  13. X. X. Yi, X. H. Su, and L. You, “Conditional quantum phase gate between two 3-state atoms,” Phys. Rev. Lett. 90, 097902 (2003).
    [CrossRef]
  14. L.-M. Duan and H. Kimble, “Scalable photonic quantum computation through cavity-assisted interactions,” Phys. Rev. Lett. 92, 127902 (2004).
    [CrossRef]
  15. X.-M. Lin, Z.-W. Zhou, M.-Y. Ye, Y.-F. Xiao, and G.-C. Guo, “One-step implementation of a multiqubit controlled-phase-flip gate,” Phys. Rev. A 73, 012323 (2006).
    [CrossRef]
  16. X. Zou, S. Zhang, K. Li, and G. Guo, “Linear optical implementation of the two-qubit controlled phase gate with conventional photon detectors,” Phys. Rev. A 75, 034302 (2007).
    [CrossRef]
  17. X. Zou, K. Li, and G. Guo, “Linear optical scheme for direct implementation of a nondestructive N-qubit controlled phase gate,” Phys. Rev. A 74, 044305 (2006).
    [CrossRef]
  18. Y.-F. Xiao, X.-B. Zou, and G.-C. Guo, “One-step implementation of an N-qubit controlled-phase gate with neutral atoms trapped in an optical cavity,” Phys. Rev. A 75, 054303 (2007).
    [CrossRef]
  19. Y. Xia, J. Song, Z.-B. Yang, and S.-B. Zheng, “Controlled implementation of two-photon controlled phase gate within a network,” Quantum Inf. Comput. 10, 0821–0828 (2010).
  20. K. Kieling, J. L. OBrien, and J. Eisert, “On photonic controlled phase gates,” New J. Phys. 12, 013003 (2010).
    [CrossRef]
  21. K. Lemr, a. Černoch, J. Soubusta, K. Kieling, J. Eisert, and M. Dušek, “Experimental implementation of the optimal linear-optical controlled phase gate,” Phys. Rev. Lett. 106, 013602 (2011).
    [CrossRef]
  22. M.-F. Wang, N.-Q. Jiang, Q.-L. Jin, and Y.-Z. Zheng, “Continuous-variable controlled-Z gate using an atomic ensemble,” Phys. Rev. A 83, 062339 (2011).
    [CrossRef]
  23. R. Ukai, S. Yokoyama, J.-i. Yoshikawa, P. van Loock, and A. Furusawa, “Demonstration of a controlled-phase gate for continuous-variable one-way quantum computation,” Phys. Rev. Lett. 107, 250501 (2011).
    [CrossRef]
  24. X.-s. Ma, S. Zotter, N. Tetik, A. Qarry, T. Jennewein, and A. Zeilinger, “A high-speed tunable beam splitter for feed-forward photonic quantum information processing,” Opt. Express 19, 22723–22730 (2011).
    [CrossRef]
  25. Y. Q. Zhang, S. Zhang, K. H. Yeon, and S. C. Yu, “One-step implementation of a multiqubit controlled-phase gate with superconducting quantum interference devices coupled to a resonator,” J. Opt. Soc. Am. B 29, 300–304 (2012).
    [CrossRef]
  26. E. Nielsen, R. Muller, and M. Carroll, “Configuration interaction calculations of the controlled phase gate in double quantum dot qubits,” Phys. Rev. B 85, 035319 (2012).
    [CrossRef]
  27. P. Kok, K. Nemoto, T. C. Ralph, J. P. Dowling, and G. J. Milburn, “Linear optical quantum computing with photonic qubits,” Rev. Mod. Phys. 79, 135–174 (2007).
    [CrossRef]
  28. J.-W. Pan, Z.-B. Chen, C.-Y. Lu, H. Weinfurter, A. Zeilinger, and M. Zukowski, “Multiphoton entanglement and interferometry,” Rev. Mod. Phys. 84, 777–838 (2012).
    [CrossRef]
  29. E. Knill, R. Laflamme, and G. J. Milburn, “A scheme for efficient quantum computation with linear optics,” Nature 409, 46–52 (2001).
    [CrossRef]
  30. E. Knill, “Bounds on the probability of success of postselected nonlinear sign shifts implemented with linear optics,” Phys. Rev. A 68, 064303 (2003).
    [CrossRef]
  31. K. Nemoto and W. J. Munro, “Nearly deterministic linear optical controlled-NOT gate,” Phys. Rev. Lett. 93, 250502 (2004).
    [CrossRef]
  32. Q. Lin and J. Li, “Quantum control gates with weak cross-Kerr nonlinearity,” Phys. Rev. A 79, 022301 (2009).
    [CrossRef]
  33. Y. Xia, J. Song, P.-M. Lu, and H.-S. Song, “Efficient implementation of the two-qubit controlled phase gate with cross-Kerr nonlinearity,” J. Phys. B 44, 025503 (2011).
    [CrossRef]
  34. X.-M. Xiu, L. Dong, Y.-J. Gao, and X. X. Yi, “Nearly deterministic controlled-not gate with weak cross-Kerr nonlinearities,” Quantum Inf. Comput. 12, 0159–0170 (2012).
  35. M. O. Scully and M. S. Zubairy, Quantum Optics (Cambridge University, 1997).
  36. C. Weedbrook, S. Pirandola, R. Garca-Patrón, N. Cerf, T. Ralph, J. Shapiro, and S. Lloyd, “Gaussian quantum information,” Rev. Mod. Phys. 84, 621–669 (2012).
    [CrossRef]
  37. S. D. Barrett, P. Kok, K. Nemoto, R. G. Beausoleil, W. J. Munro, and T. P. Spiller, “Symmetry analyzer for nondestructive Bell-state detection using weak nonlinearities,” Phys. Rev. A 71, 060302(R) (2005).
  38. C. W. Gardiner and P. Zoller, Quantum Noise (Springer, 2000).
  39. M. K. Simon, Probability Distributions Involving Gaussian Random Variables, a Handbook for Engineers, Scientists and Mathematicians (Springer, 2006).
  40. W. J. Munro, K. Nemoto, and T. P. Spiller, “Weak nonlinearities: a new route to optical quantum computation,” New J. Phys. 7, 137 (2005).
    [CrossRef]
  41. S. D. Barrett and G. J. Milburn, “Quantum-information processing via a lossy bus,” Phys. Rev. A 74, 060302(R) (2006).
    [CrossRef]
  42. B. He, J. Bergou, and Y. Ren, “Universal discriminator for completely unknown optical qubits,” Phys. Rev. A 76, 032301 (2007).
    [CrossRef]
  43. Y.-B. Sheng, F.-G. Deng, and H.-Y. Zhou, “Nonlocal entanglement concentration scheme for partially entangled multipartite systems with nonlinear optics,” Phys. Rev. A 77, 062325 (2008).
    [CrossRef]
  44. Q. Lin and B. He, “Single-photon logic gates using minimal resources,” Phys. Rev. A 80, 042310 (2009).
    [CrossRef]
  45. B. He, Y. Ren, and J. Bergou, “Creation of high-quality long-distance entanglement with flexible resources,” Phys. Rev. A 79, 052323 (2009).
    [CrossRef]
  46. Y.-B. Sheng, F.-G. Deng, and G.-L. Long, “Complete hyperentangled-Bell-state analysis for quantum communication,” Phys. Rev. A 82, 032318 (2010).
    [CrossRef]
  47. B. He, Y.-H. Ren, and J. A. Bergou, “Universal entangler with photon pairs in arbitrary states,” J. Phys. B 43, 025502 (2010).
    [CrossRef]
  48. C. Wang, Y. Zhang, and G.-S. Jin, “Polarization-entanglement purification and concentration using cross-kerr nonlinearity,” Quantum Inf. Comput. 11, 0988–1002 (2011).
  49. W. Xiong and L. Ye, “Schemes for entanglement concentration of two unknown partially entangled states with cross-Kerr nonlinearity,” J. Opt. Soc. Am. B 28, 2030–2037 (2011).
    [CrossRef]
  50. Y. Xia, J. Song, P.-M. Lu, and H.-S. Song, “Effective quantum teleportation of an atomic state between two cavities with the cross-Kerr nonlinearity by interference of polarized photons,” J. Appl. Phys. 109, 103111 (2011).
    [CrossRef]
  51. Q. Guo, J. Bai, L.-Y. Cheng, X.-Q. Shao, H.-F. Wang, and S. Zhang, “Simplified optical quantum-information processing via weak cross-Kerr nonlinearities,” Phys. Rev. A 83, 054303 (2011).
    [CrossRef]
  52. F.-G. Deng, “Efficient multipartite entanglement purification with the entanglement link from a subspace,” Phys. Rev. A 84, 052312 (2011).
    [CrossRef]
  53. Y.-B. Sheng, L. Zhou, S.-M. Zhao, and B.-Y. Zheng, “Efficient single-photon-assisted entanglement concentration for partially entangled photon pairs,” Phys. Rev. A 85, 012307 (2012).
    [CrossRef]
  54. Y.-B. Sheng, L. Zhou, and S.-M. Zhao, “Efficient two-step entanglement concentration for arbitrary W states,” Phys. Rev. A 85, 042302 (2012).
    [CrossRef]
  55. X.-W. Wang, D.-Y. Zhang, S.-Q. Tang, L.-J. Xie, Z.-Y. Wang, and L.-M. Kuang, “Photonic two-qubit parity gate with tiny cross-Kerr nonlinearity,” Phys. Rev. A 85, 052326 (2012).
    [CrossRef]
  56. X.-W. Wang, D.-Y. Zhang, S.-Q. Tang, and L.-J. Xie, “Nondestructive Greenberger–Horne–Zeilinger-state analyzer,” Quantum Inf. Process. 12, 1065–1075 (2013).
    [CrossRef]
  57. P. Kok, H. Lee, and J. Dowling, “Single-photon quantum-nondemolition detectors constructed with linear optics and projective measurements,” Phys. Rev. A 66, 063814 (2002).
    [CrossRef]
  58. S. Harris and L. Hau, “Nonlinear optics at low light levels,” Phys. Rev. Lett. 82, 4611–4614 (1999).
    [CrossRef]
  59. D. Braje, V. Balić, G. Yin, and S. Harris, “Low-light-level nonlinear optics with slow light,” Phys. Rev. A 68, 041801(R) (2003).
    [CrossRef]
  60. W. J. Munro, K. Nemoto, R. G. Beausoleil, and T. P. Spiller, “High-efficiency quantum-nondemolition single-photon-number-resolving detector,” Phys. Rev. A 71, 033819 (2005).
    [CrossRef]
  61. T. Kippenberg, S. Spillane, and K. Vahala, “Kerr-nonlinearity optical parametric oscillation in an ultrahigh-Q toroid microcavity,” Phys. Rev. Lett. 93, 083904 (2004).
    [CrossRef]
  62. X. Li, P. Voss, J. Sharping, and P. Kumar, “Optical-fiber source of polarization-entangled photons in the 1550 nm telecom band,” Phys. Rev. Lett. 94, 053601 (2005).
    [CrossRef]
  63. P. Grangier, J. A. Levenson, and J.-P. Poizat, “Quantum non-demolition measurements in optics,” Nature 396, 537–542 (1998).
    [CrossRef]
  64. H. F. Hofmann, K. Kojima, S. Takeuchi, and K. Sasaki, “Optimized phase switching using a single-atom nonlinearity,” J. Opt. B 5, 218–221 (2003).
    [CrossRef]
  65. I. Fushman, D. Englund, A. Faraon, N. Stoltz, P. Petroff, and J. Vuckovic, “Controlled phase shifts with a single quantum dot,” Science 320, 769–772 (2008).
    [CrossRef]
  66. H.-Y. Lo, P.-C. Su, and Y.-F. Chen, “Low-light-level cross-phase modulation by quantum interference,” Phys. Rev. A 81, 053829 (2010).
    [CrossRef]
  67. J. Gea-Banacloche, “Impossibility of large phase shifts via the giant Kerr effect with single-photon wave packets,” Phys. Rev. A 81, 043823 (2010).
    [CrossRef]
  68. J. Shapiro, “Single-photon Kerr nonlinearities do not help quantum computation,” Phys. Rev. A 73, 062305 (2006).
    [CrossRef]
  69. J. H. Shapiro and M. Razavi, “Continuous-time cross-phase modulation and quantum computation,” New J. Phys. 9, 16 (2007).
    [CrossRef]
  70. B. He, Q. Lin, and C. Simon, “Cross-Kerr nonlinearity between continuous-mode coherent states and single photons,” Phys. Rev. A 83, 053826 (2011).
    [CrossRef]
  71. A. Feizpour, X. Xing, and A. M. Steinberg, “Amplifying single-photon nonlinearity using weak measurements,” Phys. Rev. Lett. 107, 133603 (2011).
    [CrossRef]
  72. M. Siomau, A. A. Kamli, S. A. Moiseev, and B. C. Sanders, “Entanglement creation with negative index metamaterials,” Phys. Rev. A 85, 050303(R) (2012).
    [CrossRef]
  73. X.-M. Jin, J.-G. Ren, B. Yang, Z.-H. Yi, F. Zhou, X.-F. Xu, S.-K. Wang, D. Yang, Y.-F. Hu, S. Jiang, T. Yang, H. Yin, K. Chen, C.-Z. Peng, and J.-W. Pan, “Experimental free-space quantum teleportation,” Nat. Photonics 4, 376–381 (2010).
    [CrossRef]
  74. S. Phoenix, “Wave-packet evolution in the damped oscillator,” Phys. Rev. A 41, 5132–5138 (1990).
    [CrossRef]
  75. H. Jeong, “Quantum computation using weak nonlinearities: robustness against decoherence,” Phys. Rev. A 73, 052320 (2006).
    [CrossRef]
  76. S. G. R. Louis, W. J. Munro, T. P. Spiller, and K. Nemoto, “Loss in hybrid qubit-bus couplings and gates,” Phys. Rev. A 78, 022326 (2008).
    [CrossRef]
  77. C. C. Gerry and T. Bui, “Quantum non-demolition measurement of photon number using weak nonlinearities,” Phys. Lett. A 372, 7101–7104 (2008).
    [CrossRef]
  78. X.-s. Ma, S. Zotter, J. Kofler, T. Jennewein, and A. Zeilinger, “Experimental generation of single photons via active multiplexing,” Phys. Rev. A 83, 043814 (2011).
    [CrossRef]

2013

X.-W. Wang, D.-Y. Zhang, S.-Q. Tang, and L.-J. Xie, “Nondestructive Greenberger–Horne–Zeilinger-state analyzer,” Quantum Inf. Process. 12, 1065–1075 (2013).
[CrossRef]

2012

M. Siomau, A. A. Kamli, S. A. Moiseev, and B. C. Sanders, “Entanglement creation with negative index metamaterials,” Phys. Rev. A 85, 050303(R) (2012).
[CrossRef]

Y.-B. Sheng, L. Zhou, S.-M. Zhao, and B.-Y. Zheng, “Efficient single-photon-assisted entanglement concentration for partially entangled photon pairs,” Phys. Rev. A 85, 012307 (2012).
[CrossRef]

Y.-B. Sheng, L. Zhou, and S.-M. Zhao, “Efficient two-step entanglement concentration for arbitrary W states,” Phys. Rev. A 85, 042302 (2012).
[CrossRef]

X.-W. Wang, D.-Y. Zhang, S.-Q. Tang, L.-J. Xie, Z.-Y. Wang, and L.-M. Kuang, “Photonic two-qubit parity gate with tiny cross-Kerr nonlinearity,” Phys. Rev. A 85, 052326 (2012).
[CrossRef]

Y. Q. Zhang, S. Zhang, K. H. Yeon, and S. C. Yu, “One-step implementation of a multiqubit controlled-phase gate with superconducting quantum interference devices coupled to a resonator,” J. Opt. Soc. Am. B 29, 300–304 (2012).
[CrossRef]

E. Nielsen, R. Muller, and M. Carroll, “Configuration interaction calculations of the controlled phase gate in double quantum dot qubits,” Phys. Rev. B 85, 035319 (2012).
[CrossRef]

J.-W. Pan, Z.-B. Chen, C.-Y. Lu, H. Weinfurter, A. Zeilinger, and M. Zukowski, “Multiphoton entanglement and interferometry,” Rev. Mod. Phys. 84, 777–838 (2012).
[CrossRef]

X.-M. Xiu, L. Dong, Y.-J. Gao, and X. X. Yi, “Nearly deterministic controlled-not gate with weak cross-Kerr nonlinearities,” Quantum Inf. Comput. 12, 0159–0170 (2012).

C. Weedbrook, S. Pirandola, R. Garca-Patrón, N. Cerf, T. Ralph, J. Shapiro, and S. Lloyd, “Gaussian quantum information,” Rev. Mod. Phys. 84, 621–669 (2012).
[CrossRef]

2011

K. Lemr, a. Černoch, J. Soubusta, K. Kieling, J. Eisert, and M. Dušek, “Experimental implementation of the optimal linear-optical controlled phase gate,” Phys. Rev. Lett. 106, 013602 (2011).
[CrossRef]

M.-F. Wang, N.-Q. Jiang, Q.-L. Jin, and Y.-Z. Zheng, “Continuous-variable controlled-Z gate using an atomic ensemble,” Phys. Rev. A 83, 062339 (2011).
[CrossRef]

R. Ukai, S. Yokoyama, J.-i. Yoshikawa, P. van Loock, and A. Furusawa, “Demonstration of a controlled-phase gate for continuous-variable one-way quantum computation,” Phys. Rev. Lett. 107, 250501 (2011).
[CrossRef]

X.-s. Ma, S. Zotter, N. Tetik, A. Qarry, T. Jennewein, and A. Zeilinger, “A high-speed tunable beam splitter for feed-forward photonic quantum information processing,” Opt. Express 19, 22723–22730 (2011).
[CrossRef]

M. Mariantoni, H. Wang, T. Yamamoto, M. Neeley, R. C. Bialczak, Y. Chen, M. Lenander, E. Lucero, A. D. OConnell, D. Sank, M. Weides, J. Wenner, Y. Yin, J. Zhao, A. N. Korotkov, A. N. Cleland, and J. M. Martinis, “Implementing the quantum von Neumann architecture with superconducting circuits,” Science 334, 61–65 (2011).
[CrossRef]

C. Wang, Y. Zhang, and G.-S. Jin, “Polarization-entanglement purification and concentration using cross-kerr nonlinearity,” Quantum Inf. Comput. 11, 0988–1002 (2011).

W. Xiong and L. Ye, “Schemes for entanglement concentration of two unknown partially entangled states with cross-Kerr nonlinearity,” J. Opt. Soc. Am. B 28, 2030–2037 (2011).
[CrossRef]

Y. Xia, J. Song, P.-M. Lu, and H.-S. Song, “Effective quantum teleportation of an atomic state between two cavities with the cross-Kerr nonlinearity by interference of polarized photons,” J. Appl. Phys. 109, 103111 (2011).
[CrossRef]

Q. Guo, J. Bai, L.-Y. Cheng, X.-Q. Shao, H.-F. Wang, and S. Zhang, “Simplified optical quantum-information processing via weak cross-Kerr nonlinearities,” Phys. Rev. A 83, 054303 (2011).
[CrossRef]

F.-G. Deng, “Efficient multipartite entanglement purification with the entanglement link from a subspace,” Phys. Rev. A 84, 052312 (2011).
[CrossRef]

Y. Xia, J. Song, P.-M. Lu, and H.-S. Song, “Efficient implementation of the two-qubit controlled phase gate with cross-Kerr nonlinearity,” J. Phys. B 44, 025503 (2011).
[CrossRef]

B. He, Q. Lin, and C. Simon, “Cross-Kerr nonlinearity between continuous-mode coherent states and single photons,” Phys. Rev. A 83, 053826 (2011).
[CrossRef]

A. Feizpour, X. Xing, and A. M. Steinberg, “Amplifying single-photon nonlinearity using weak measurements,” Phys. Rev. Lett. 107, 133603 (2011).
[CrossRef]

X.-s. Ma, S. Zotter, J. Kofler, T. Jennewein, and A. Zeilinger, “Experimental generation of single photons via active multiplexing,” Phys. Rev. A 83, 043814 (2011).
[CrossRef]

2010

X.-M. Jin, J.-G. Ren, B. Yang, Z.-H. Yi, F. Zhou, X.-F. Xu, S.-K. Wang, D. Yang, Y.-F. Hu, S. Jiang, T. Yang, H. Yin, K. Chen, C.-Z. Peng, and J.-W. Pan, “Experimental free-space quantum teleportation,” Nat. Photonics 4, 376–381 (2010).
[CrossRef]

H.-Y. Lo, P.-C. Su, and Y.-F. Chen, “Low-light-level cross-phase modulation by quantum interference,” Phys. Rev. A 81, 053829 (2010).
[CrossRef]

J. Gea-Banacloche, “Impossibility of large phase shifts via the giant Kerr effect with single-photon wave packets,” Phys. Rev. A 81, 043823 (2010).
[CrossRef]

Y.-B. Sheng, F.-G. Deng, and G.-L. Long, “Complete hyperentangled-Bell-state analysis for quantum communication,” Phys. Rev. A 82, 032318 (2010).
[CrossRef]

B. He, Y.-H. Ren, and J. A. Bergou, “Universal entangler with photon pairs in arbitrary states,” J. Phys. B 43, 025502 (2010).
[CrossRef]

Y. Xia, J. Song, Z.-B. Yang, and S.-B. Zheng, “Controlled implementation of two-photon controlled phase gate within a network,” Quantum Inf. Comput. 10, 0821–0828 (2010).

K. Kieling, J. L. OBrien, and J. Eisert, “On photonic controlled phase gates,” New J. Phys. 12, 013003 (2010).
[CrossRef]

2009

Q. Lin and J. Li, “Quantum control gates with weak cross-Kerr nonlinearity,” Phys. Rev. A 79, 022301 (2009).
[CrossRef]

Q. Lin and B. He, “Single-photon logic gates using minimal resources,” Phys. Rev. A 80, 042310 (2009).
[CrossRef]

B. He, Y. Ren, and J. Bergou, “Creation of high-quality long-distance entanglement with flexible resources,” Phys. Rev. A 79, 052323 (2009).
[CrossRef]

2008

Y.-B. Sheng, F.-G. Deng, and H.-Y. Zhou, “Nonlocal entanglement concentration scheme for partially entangled multipartite systems with nonlinear optics,” Phys. Rev. A 77, 062325 (2008).
[CrossRef]

I. Fushman, D. Englund, A. Faraon, N. Stoltz, P. Petroff, and J. Vuckovic, “Controlled phase shifts with a single quantum dot,” Science 320, 769–772 (2008).
[CrossRef]

K. S. Choi, H. Deng, J. Laurat, and H. J. Kimble, “Mapping photonic entanglement into and out of a quantum memory,” Nature 452, 67–71 (2008).
[CrossRef]

S. G. R. Louis, W. J. Munro, T. P. Spiller, and K. Nemoto, “Loss in hybrid qubit-bus couplings and gates,” Phys. Rev. A 78, 022326 (2008).
[CrossRef]

C. C. Gerry and T. Bui, “Quantum non-demolition measurement of photon number using weak nonlinearities,” Phys. Lett. A 372, 7101–7104 (2008).
[CrossRef]

2007

X. Zou, S. Zhang, K. Li, and G. Guo, “Linear optical implementation of the two-qubit controlled phase gate with conventional photon detectors,” Phys. Rev. A 75, 034302 (2007).
[CrossRef]

P. Kok, K. Nemoto, T. C. Ralph, J. P. Dowling, and G. J. Milburn, “Linear optical quantum computing with photonic qubits,” Rev. Mod. Phys. 79, 135–174 (2007).
[CrossRef]

Y.-F. Xiao, X.-B. Zou, and G.-C. Guo, “One-step implementation of an N-qubit controlled-phase gate with neutral atoms trapped in an optical cavity,” Phys. Rev. A 75, 054303 (2007).
[CrossRef]

J. H. Shapiro and M. Razavi, “Continuous-time cross-phase modulation and quantum computation,” New J. Phys. 9, 16 (2007).
[CrossRef]

B. He, J. Bergou, and Y. Ren, “Universal discriminator for completely unknown optical qubits,” Phys. Rev. A 76, 032301 (2007).
[CrossRef]

2006

S. D. Barrett and G. J. Milburn, “Quantum-information processing via a lossy bus,” Phys. Rev. A 74, 060302(R) (2006).
[CrossRef]

J. Shapiro, “Single-photon Kerr nonlinearities do not help quantum computation,” Phys. Rev. A 73, 062305 (2006).
[CrossRef]

X. Zou, K. Li, and G. Guo, “Linear optical scheme for direct implementation of a nondestructive N-qubit controlled phase gate,” Phys. Rev. A 74, 044305 (2006).
[CrossRef]

X.-M. Lin, Z.-W. Zhou, M.-Y. Ye, Y.-F. Xiao, and G.-C. Guo, “One-step implementation of a multiqubit controlled-phase-flip gate,” Phys. Rev. A 73, 012323 (2006).
[CrossRef]

H. Jeong, “Quantum computation using weak nonlinearities: robustness against decoherence,” Phys. Rev. A 73, 052320 (2006).
[CrossRef]

2005

S. D. Barrett, P. Kok, K. Nemoto, R. G. Beausoleil, W. J. Munro, and T. P. Spiller, “Symmetry analyzer for nondestructive Bell-state detection using weak nonlinearities,” Phys. Rev. A 71, 060302(R) (2005).

W. J. Munro, K. Nemoto, and T. P. Spiller, “Weak nonlinearities: a new route to optical quantum computation,” New J. Phys. 7, 137 (2005).
[CrossRef]

W. J. Munro, K. Nemoto, R. G. Beausoleil, and T. P. Spiller, “High-efficiency quantum-nondemolition single-photon-number-resolving detector,” Phys. Rev. A 71, 033819 (2005).
[CrossRef]

X. Li, P. Voss, J. Sharping, and P. Kumar, “Optical-fiber source of polarization-entangled photons in the 1550 nm telecom band,” Phys. Rev. Lett. 94, 053601 (2005).
[CrossRef]

2004

T. Kippenberg, S. Spillane, and K. Vahala, “Kerr-nonlinearity optical parametric oscillation in an ultrahigh-Q toroid microcavity,” Phys. Rev. Lett. 93, 083904 (2004).
[CrossRef]

K. Nemoto and W. J. Munro, “Nearly deterministic linear optical controlled-NOT gate,” Phys. Rev. Lett. 93, 250502 (2004).
[CrossRef]

L.-M. Duan and H. Kimble, “Scalable photonic quantum computation through cavity-assisted interactions,” Phys. Rev. Lett. 92, 127902 (2004).
[CrossRef]

2003

F. Schmidt-Kaler, H. Häffner, M. Riebe, S. Gulde, G. P. T. Lancaster, T. Deuschle, C. Becher, C. F. Roos, J. Eschner, and R. Blatt, “Realization of the Cirac–Zoller controlled-NOT quantum gate,” Nature 422, 408–411 (2003).
[CrossRef]

L. You, X. X. Yi, and X. H. Su, “Quantum logic between atoms inside a high-Q optical cavity,” Phys. Rev. A 67, 032308 (2003).
[CrossRef]

X. X. Yi, X. H. Su, and L. You, “Conditional quantum phase gate between two 3-state atoms,” Phys. Rev. Lett. 90, 097902 (2003).
[CrossRef]

E. Knill, “Bounds on the probability of success of postselected nonlinear sign shifts implemented with linear optics,” Phys. Rev. A 68, 064303 (2003).
[CrossRef]

D. Braje, V. Balić, G. Yin, and S. Harris, “Low-light-level nonlinear optics with slow light,” Phys. Rev. A 68, 041801(R) (2003).
[CrossRef]

H. F. Hofmann, K. Kojima, S. Takeuchi, and K. Sasaki, “Optimized phase switching using a single-atom nonlinearity,” J. Opt. B 5, 218–221 (2003).
[CrossRef]

2002

P. Kok, H. Lee, and J. Dowling, “Single-photon quantum-nondemolition detectors constructed with linear optics and projective measurements,” Phys. Rev. A 66, 063814 (2002).
[CrossRef]

2001

E. Knill, R. Laflamme, and G. J. Milburn, “A scheme for efficient quantum computation with linear optics,” Nature 409, 46–52 (2001).
[CrossRef]

M. Koashi, T. Yamamoto, and N. Imoto, “Probabilistic manipulation of entangled photons,” Phys. Rev. A 63, 030301(R) (2001).
[CrossRef]

T. Pittman, B. Jacobs, and J. Franson, “Probabilistic quantum logic operations using polarizing beam splitters,” Phys. Rev. A 64, 062311 (2001).
[CrossRef]

1999

A. Sørensen and K. Mølmer, “Quantum computation with ions in thermal motion,” Phys. Rev. Lett. 82, 1971–1974 (1999).
[CrossRef]

S. Harris and L. Hau, “Nonlinear optics at low light levels,” Phys. Rev. Lett. 82, 4611–4614 (1999).
[CrossRef]

1998

P. Grangier, J. A. Levenson, and J.-P. Poizat, “Quantum non-demolition measurements in optics,” Nature 396, 537–542 (1998).
[CrossRef]

1995

A. Barenco, D. Deutsch, A. Ekert, and R. Jozsa, “Conditional quantum dynamics and logic gates,” Phys. Rev. Lett. 74, 4083–4086 (1995).
[CrossRef]

J. Cirac and P. Zoller, “Quantum computations with cold trapped ions,” Phys. Rev. Lett. 74, 4091–4094 (1995).
[CrossRef]

I. Chuang and Y. Yamamoto, “Simple quantum computer,” Phys. Rev. A 52, 3489–3496 (1995).
[CrossRef]

Q. A. Turchette, C. J. Hood, W. Lange, H. Mabuchi, and H. J. Kimble, “Measurement of conditional phase shifts for quantum logic,” Phys. Rev. Lett. 75, 4710–4713 (1995).
[CrossRef]

1990

S. Phoenix, “Wave-packet evolution in the damped oscillator,” Phys. Rev. A 41, 5132–5138 (1990).
[CrossRef]

Bai, J.

Q. Guo, J. Bai, L.-Y. Cheng, X.-Q. Shao, H.-F. Wang, and S. Zhang, “Simplified optical quantum-information processing via weak cross-Kerr nonlinearities,” Phys. Rev. A 83, 054303 (2011).
[CrossRef]

Balic, V.

D. Braje, V. Balić, G. Yin, and S. Harris, “Low-light-level nonlinear optics with slow light,” Phys. Rev. A 68, 041801(R) (2003).
[CrossRef]

Barenco, A.

A. Barenco, D. Deutsch, A. Ekert, and R. Jozsa, “Conditional quantum dynamics and logic gates,” Phys. Rev. Lett. 74, 4083–4086 (1995).
[CrossRef]

Barrett, S. D.

S. D. Barrett and G. J. Milburn, “Quantum-information processing via a lossy bus,” Phys. Rev. A 74, 060302(R) (2006).
[CrossRef]

S. D. Barrett, P. Kok, K. Nemoto, R. G. Beausoleil, W. J. Munro, and T. P. Spiller, “Symmetry analyzer for nondestructive Bell-state detection using weak nonlinearities,” Phys. Rev. A 71, 060302(R) (2005).

Beausoleil, R. G.

S. D. Barrett, P. Kok, K. Nemoto, R. G. Beausoleil, W. J. Munro, and T. P. Spiller, “Symmetry analyzer for nondestructive Bell-state detection using weak nonlinearities,” Phys. Rev. A 71, 060302(R) (2005).

W. J. Munro, K. Nemoto, R. G. Beausoleil, and T. P. Spiller, “High-efficiency quantum-nondemolition single-photon-number-resolving detector,” Phys. Rev. A 71, 033819 (2005).
[CrossRef]

Becher, C.

F. Schmidt-Kaler, H. Häffner, M. Riebe, S. Gulde, G. P. T. Lancaster, T. Deuschle, C. Becher, C. F. Roos, J. Eschner, and R. Blatt, “Realization of the Cirac–Zoller controlled-NOT quantum gate,” Nature 422, 408–411 (2003).
[CrossRef]

Bergou, J.

B. He, Y. Ren, and J. Bergou, “Creation of high-quality long-distance entanglement with flexible resources,” Phys. Rev. A 79, 052323 (2009).
[CrossRef]

B. He, J. Bergou, and Y. Ren, “Universal discriminator for completely unknown optical qubits,” Phys. Rev. A 76, 032301 (2007).
[CrossRef]

Bergou, J. A.

B. He, Y.-H. Ren, and J. A. Bergou, “Universal entangler with photon pairs in arbitrary states,” J. Phys. B 43, 025502 (2010).
[CrossRef]

Bialczak, R. C.

M. Mariantoni, H. Wang, T. Yamamoto, M. Neeley, R. C. Bialczak, Y. Chen, M. Lenander, E. Lucero, A. D. OConnell, D. Sank, M. Weides, J. Wenner, Y. Yin, J. Zhao, A. N. Korotkov, A. N. Cleland, and J. M. Martinis, “Implementing the quantum von Neumann architecture with superconducting circuits,” Science 334, 61–65 (2011).
[CrossRef]

Blatt, R.

F. Schmidt-Kaler, H. Häffner, M. Riebe, S. Gulde, G. P. T. Lancaster, T. Deuschle, C. Becher, C. F. Roos, J. Eschner, and R. Blatt, “Realization of the Cirac–Zoller controlled-NOT quantum gate,” Nature 422, 408–411 (2003).
[CrossRef]

Braje, D.

D. Braje, V. Balić, G. Yin, and S. Harris, “Low-light-level nonlinear optics with slow light,” Phys. Rev. A 68, 041801(R) (2003).
[CrossRef]

Bui, T.

C. C. Gerry and T. Bui, “Quantum non-demolition measurement of photon number using weak nonlinearities,” Phys. Lett. A 372, 7101–7104 (2008).
[CrossRef]

Carroll, M.

E. Nielsen, R. Muller, and M. Carroll, “Configuration interaction calculations of the controlled phase gate in double quantum dot qubits,” Phys. Rev. B 85, 035319 (2012).
[CrossRef]

Cerf, N.

C. Weedbrook, S. Pirandola, R. Garca-Patrón, N. Cerf, T. Ralph, J. Shapiro, and S. Lloyd, “Gaussian quantum information,” Rev. Mod. Phys. 84, 621–669 (2012).
[CrossRef]

Cernoch, a.

K. Lemr, a. Černoch, J. Soubusta, K. Kieling, J. Eisert, and M. Dušek, “Experimental implementation of the optimal linear-optical controlled phase gate,” Phys. Rev. Lett. 106, 013602 (2011).
[CrossRef]

Chen, K.

X.-M. Jin, J.-G. Ren, B. Yang, Z.-H. Yi, F. Zhou, X.-F. Xu, S.-K. Wang, D. Yang, Y.-F. Hu, S. Jiang, T. Yang, H. Yin, K. Chen, C.-Z. Peng, and J.-W. Pan, “Experimental free-space quantum teleportation,” Nat. Photonics 4, 376–381 (2010).
[CrossRef]

Chen, Y.

M. Mariantoni, H. Wang, T. Yamamoto, M. Neeley, R. C. Bialczak, Y. Chen, M. Lenander, E. Lucero, A. D. OConnell, D. Sank, M. Weides, J. Wenner, Y. Yin, J. Zhao, A. N. Korotkov, A. N. Cleland, and J. M. Martinis, “Implementing the quantum von Neumann architecture with superconducting circuits,” Science 334, 61–65 (2011).
[CrossRef]

Chen, Y.-F.

H.-Y. Lo, P.-C. Su, and Y.-F. Chen, “Low-light-level cross-phase modulation by quantum interference,” Phys. Rev. A 81, 053829 (2010).
[CrossRef]

Chen, Z.-B.

J.-W. Pan, Z.-B. Chen, C.-Y. Lu, H. Weinfurter, A. Zeilinger, and M. Zukowski, “Multiphoton entanglement and interferometry,” Rev. Mod. Phys. 84, 777–838 (2012).
[CrossRef]

Cheng, L.-Y.

Q. Guo, J. Bai, L.-Y. Cheng, X.-Q. Shao, H.-F. Wang, and S. Zhang, “Simplified optical quantum-information processing via weak cross-Kerr nonlinearities,” Phys. Rev. A 83, 054303 (2011).
[CrossRef]

Choi, K. S.

K. S. Choi, H. Deng, J. Laurat, and H. J. Kimble, “Mapping photonic entanglement into and out of a quantum memory,” Nature 452, 67–71 (2008).
[CrossRef]

Chuang, I.

I. Chuang and Y. Yamamoto, “Simple quantum computer,” Phys. Rev. A 52, 3489–3496 (1995).
[CrossRef]

Chuang, I. L.

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

Cirac, J.

J. Cirac and P. Zoller, “Quantum computations with cold trapped ions,” Phys. Rev. Lett. 74, 4091–4094 (1995).
[CrossRef]

Cleland, A. N.

M. Mariantoni, H. Wang, T. Yamamoto, M. Neeley, R. C. Bialczak, Y. Chen, M. Lenander, E. Lucero, A. D. OConnell, D. Sank, M. Weides, J. Wenner, Y. Yin, J. Zhao, A. N. Korotkov, A. N. Cleland, and J. M. Martinis, “Implementing the quantum von Neumann architecture with superconducting circuits,” Science 334, 61–65 (2011).
[CrossRef]

Deng, F.-G.

F.-G. Deng, “Efficient multipartite entanglement purification with the entanglement link from a subspace,” Phys. Rev. A 84, 052312 (2011).
[CrossRef]

Y.-B. Sheng, F.-G. Deng, and G.-L. Long, “Complete hyperentangled-Bell-state analysis for quantum communication,” Phys. Rev. A 82, 032318 (2010).
[CrossRef]

Y.-B. Sheng, F.-G. Deng, and H.-Y. Zhou, “Nonlocal entanglement concentration scheme for partially entangled multipartite systems with nonlinear optics,” Phys. Rev. A 77, 062325 (2008).
[CrossRef]

Deng, H.

K. S. Choi, H. Deng, J. Laurat, and H. J. Kimble, “Mapping photonic entanglement into and out of a quantum memory,” Nature 452, 67–71 (2008).
[CrossRef]

Deuschle, T.

F. Schmidt-Kaler, H. Häffner, M. Riebe, S. Gulde, G. P. T. Lancaster, T. Deuschle, C. Becher, C. F. Roos, J. Eschner, and R. Blatt, “Realization of the Cirac–Zoller controlled-NOT quantum gate,” Nature 422, 408–411 (2003).
[CrossRef]

Deutsch, D.

A. Barenco, D. Deutsch, A. Ekert, and R. Jozsa, “Conditional quantum dynamics and logic gates,” Phys. Rev. Lett. 74, 4083–4086 (1995).
[CrossRef]

Dong, L.

X.-M. Xiu, L. Dong, Y.-J. Gao, and X. X. Yi, “Nearly deterministic controlled-not gate with weak cross-Kerr nonlinearities,” Quantum Inf. Comput. 12, 0159–0170 (2012).

Dowling, J.

P. Kok, H. Lee, and J. Dowling, “Single-photon quantum-nondemolition detectors constructed with linear optics and projective measurements,” Phys. Rev. A 66, 063814 (2002).
[CrossRef]

Dowling, J. P.

P. Kok, K. Nemoto, T. C. Ralph, J. P. Dowling, and G. J. Milburn, “Linear optical quantum computing with photonic qubits,” Rev. Mod. Phys. 79, 135–174 (2007).
[CrossRef]

Duan, L.-M.

L.-M. Duan and H. Kimble, “Scalable photonic quantum computation through cavity-assisted interactions,” Phys. Rev. Lett. 92, 127902 (2004).
[CrossRef]

Dušek, M.

K. Lemr, a. Černoch, J. Soubusta, K. Kieling, J. Eisert, and M. Dušek, “Experimental implementation of the optimal linear-optical controlled phase gate,” Phys. Rev. Lett. 106, 013602 (2011).
[CrossRef]

Eisert, J.

K. Lemr, a. Černoch, J. Soubusta, K. Kieling, J. Eisert, and M. Dušek, “Experimental implementation of the optimal linear-optical controlled phase gate,” Phys. Rev. Lett. 106, 013602 (2011).
[CrossRef]

K. Kieling, J. L. OBrien, and J. Eisert, “On photonic controlled phase gates,” New J. Phys. 12, 013003 (2010).
[CrossRef]

Ekert, A.

A. Barenco, D. Deutsch, A. Ekert, and R. Jozsa, “Conditional quantum dynamics and logic gates,” Phys. Rev. Lett. 74, 4083–4086 (1995).
[CrossRef]

Englund, D.

I. Fushman, D. Englund, A. Faraon, N. Stoltz, P. Petroff, and J. Vuckovic, “Controlled phase shifts with a single quantum dot,” Science 320, 769–772 (2008).
[CrossRef]

Eschner, J.

F. Schmidt-Kaler, H. Häffner, M. Riebe, S. Gulde, G. P. T. Lancaster, T. Deuschle, C. Becher, C. F. Roos, J. Eschner, and R. Blatt, “Realization of the Cirac–Zoller controlled-NOT quantum gate,” Nature 422, 408–411 (2003).
[CrossRef]

Faraon, A.

I. Fushman, D. Englund, A. Faraon, N. Stoltz, P. Petroff, and J. Vuckovic, “Controlled phase shifts with a single quantum dot,” Science 320, 769–772 (2008).
[CrossRef]

Feizpour, A.

A. Feizpour, X. Xing, and A. M. Steinberg, “Amplifying single-photon nonlinearity using weak measurements,” Phys. Rev. Lett. 107, 133603 (2011).
[CrossRef]

Franson, J.

T. Pittman, B. Jacobs, and J. Franson, “Probabilistic quantum logic operations using polarizing beam splitters,” Phys. Rev. A 64, 062311 (2001).
[CrossRef]

Furusawa, A.

R. Ukai, S. Yokoyama, J.-i. Yoshikawa, P. van Loock, and A. Furusawa, “Demonstration of a controlled-phase gate for continuous-variable one-way quantum computation,” Phys. Rev. Lett. 107, 250501 (2011).
[CrossRef]

Fushman, I.

I. Fushman, D. Englund, A. Faraon, N. Stoltz, P. Petroff, and J. Vuckovic, “Controlled phase shifts with a single quantum dot,” Science 320, 769–772 (2008).
[CrossRef]

Gao, Y.-J.

X.-M. Xiu, L. Dong, Y.-J. Gao, and X. X. Yi, “Nearly deterministic controlled-not gate with weak cross-Kerr nonlinearities,” Quantum Inf. Comput. 12, 0159–0170 (2012).

Garca-Patrón, R.

C. Weedbrook, S. Pirandola, R. Garca-Patrón, N. Cerf, T. Ralph, J. Shapiro, and S. Lloyd, “Gaussian quantum information,” Rev. Mod. Phys. 84, 621–669 (2012).
[CrossRef]

Gardiner, C. W.

C. W. Gardiner and P. Zoller, Quantum Noise (Springer, 2000).

Gea-Banacloche, J.

J. Gea-Banacloche, “Impossibility of large phase shifts via the giant Kerr effect with single-photon wave packets,” Phys. Rev. A 81, 043823 (2010).
[CrossRef]

Gerry, C. C.

C. C. Gerry and T. Bui, “Quantum non-demolition measurement of photon number using weak nonlinearities,” Phys. Lett. A 372, 7101–7104 (2008).
[CrossRef]

Grangier, P.

P. Grangier, J. A. Levenson, and J.-P. Poizat, “Quantum non-demolition measurements in optics,” Nature 396, 537–542 (1998).
[CrossRef]

Gulde, S.

F. Schmidt-Kaler, H. Häffner, M. Riebe, S. Gulde, G. P. T. Lancaster, T. Deuschle, C. Becher, C. F. Roos, J. Eschner, and R. Blatt, “Realization of the Cirac–Zoller controlled-NOT quantum gate,” Nature 422, 408–411 (2003).
[CrossRef]

Guo, G.

X. Zou, S. Zhang, K. Li, and G. Guo, “Linear optical implementation of the two-qubit controlled phase gate with conventional photon detectors,” Phys. Rev. A 75, 034302 (2007).
[CrossRef]

X. Zou, K. Li, and G. Guo, “Linear optical scheme for direct implementation of a nondestructive N-qubit controlled phase gate,” Phys. Rev. A 74, 044305 (2006).
[CrossRef]

Guo, G.-C.

Y.-F. Xiao, X.-B. Zou, and G.-C. Guo, “One-step implementation of an N-qubit controlled-phase gate with neutral atoms trapped in an optical cavity,” Phys. Rev. A 75, 054303 (2007).
[CrossRef]

X.-M. Lin, Z.-W. Zhou, M.-Y. Ye, Y.-F. Xiao, and G.-C. Guo, “One-step implementation of a multiqubit controlled-phase-flip gate,” Phys. Rev. A 73, 012323 (2006).
[CrossRef]

Guo, Q.

Q. Guo, J. Bai, L.-Y. Cheng, X.-Q. Shao, H.-F. Wang, and S. Zhang, “Simplified optical quantum-information processing via weak cross-Kerr nonlinearities,” Phys. Rev. A 83, 054303 (2011).
[CrossRef]

Häffner, H.

F. Schmidt-Kaler, H. Häffner, M. Riebe, S. Gulde, G. P. T. Lancaster, T. Deuschle, C. Becher, C. F. Roos, J. Eschner, and R. Blatt, “Realization of the Cirac–Zoller controlled-NOT quantum gate,” Nature 422, 408–411 (2003).
[CrossRef]

Harris, S.

D. Braje, V. Balić, G. Yin, and S. Harris, “Low-light-level nonlinear optics with slow light,” Phys. Rev. A 68, 041801(R) (2003).
[CrossRef]

S. Harris and L. Hau, “Nonlinear optics at low light levels,” Phys. Rev. Lett. 82, 4611–4614 (1999).
[CrossRef]

Hau, L.

S. Harris and L. Hau, “Nonlinear optics at low light levels,” Phys. Rev. Lett. 82, 4611–4614 (1999).
[CrossRef]

He, B.

B. He, Q. Lin, and C. Simon, “Cross-Kerr nonlinearity between continuous-mode coherent states and single photons,” Phys. Rev. A 83, 053826 (2011).
[CrossRef]

B. He, Y.-H. Ren, and J. A. Bergou, “Universal entangler with photon pairs in arbitrary states,” J. Phys. B 43, 025502 (2010).
[CrossRef]

Q. Lin and B. He, “Single-photon logic gates using minimal resources,” Phys. Rev. A 80, 042310 (2009).
[CrossRef]

B. He, Y. Ren, and J. Bergou, “Creation of high-quality long-distance entanglement with flexible resources,” Phys. Rev. A 79, 052323 (2009).
[CrossRef]

B. He, J. Bergou, and Y. Ren, “Universal discriminator for completely unknown optical qubits,” Phys. Rev. A 76, 032301 (2007).
[CrossRef]

Hofmann, H. F.

H. F. Hofmann, K. Kojima, S. Takeuchi, and K. Sasaki, “Optimized phase switching using a single-atom nonlinearity,” J. Opt. B 5, 218–221 (2003).
[CrossRef]

Hood, C. J.

Q. A. Turchette, C. J. Hood, W. Lange, H. Mabuchi, and H. J. Kimble, “Measurement of conditional phase shifts for quantum logic,” Phys. Rev. Lett. 75, 4710–4713 (1995).
[CrossRef]

Hu, Y.-F.

X.-M. Jin, J.-G. Ren, B. Yang, Z.-H. Yi, F. Zhou, X.-F. Xu, S.-K. Wang, D. Yang, Y.-F. Hu, S. Jiang, T. Yang, H. Yin, K. Chen, C.-Z. Peng, and J.-W. Pan, “Experimental free-space quantum teleportation,” Nat. Photonics 4, 376–381 (2010).
[CrossRef]

Imoto, N.

M. Koashi, T. Yamamoto, and N. Imoto, “Probabilistic manipulation of entangled photons,” Phys. Rev. A 63, 030301(R) (2001).
[CrossRef]

Jacobs, B.

T. Pittman, B. Jacobs, and J. Franson, “Probabilistic quantum logic operations using polarizing beam splitters,” Phys. Rev. A 64, 062311 (2001).
[CrossRef]

Jennewein, T.

X.-s. Ma, S. Zotter, N. Tetik, A. Qarry, T. Jennewein, and A. Zeilinger, “A high-speed tunable beam splitter for feed-forward photonic quantum information processing,” Opt. Express 19, 22723–22730 (2011).
[CrossRef]

X.-s. Ma, S. Zotter, J. Kofler, T. Jennewein, and A. Zeilinger, “Experimental generation of single photons via active multiplexing,” Phys. Rev. A 83, 043814 (2011).
[CrossRef]

Jeong, H.

H. Jeong, “Quantum computation using weak nonlinearities: robustness against decoherence,” Phys. Rev. A 73, 052320 (2006).
[CrossRef]

Jiang, N.-Q.

M.-F. Wang, N.-Q. Jiang, Q.-L. Jin, and Y.-Z. Zheng, “Continuous-variable controlled-Z gate using an atomic ensemble,” Phys. Rev. A 83, 062339 (2011).
[CrossRef]

Jiang, S.

X.-M. Jin, J.-G. Ren, B. Yang, Z.-H. Yi, F. Zhou, X.-F. Xu, S.-K. Wang, D. Yang, Y.-F. Hu, S. Jiang, T. Yang, H. Yin, K. Chen, C.-Z. Peng, and J.-W. Pan, “Experimental free-space quantum teleportation,” Nat. Photonics 4, 376–381 (2010).
[CrossRef]

Jin, G.-S.

C. Wang, Y. Zhang, and G.-S. Jin, “Polarization-entanglement purification and concentration using cross-kerr nonlinearity,” Quantum Inf. Comput. 11, 0988–1002 (2011).

Jin, Q.-L.

M.-F. Wang, N.-Q. Jiang, Q.-L. Jin, and Y.-Z. Zheng, “Continuous-variable controlled-Z gate using an atomic ensemble,” Phys. Rev. A 83, 062339 (2011).
[CrossRef]

Jin, X.-M.

X.-M. Jin, J.-G. Ren, B. Yang, Z.-H. Yi, F. Zhou, X.-F. Xu, S.-K. Wang, D. Yang, Y.-F. Hu, S. Jiang, T. Yang, H. Yin, K. Chen, C.-Z. Peng, and J.-W. Pan, “Experimental free-space quantum teleportation,” Nat. Photonics 4, 376–381 (2010).
[CrossRef]

Jozsa, R.

A. Barenco, D. Deutsch, A. Ekert, and R. Jozsa, “Conditional quantum dynamics and logic gates,” Phys. Rev. Lett. 74, 4083–4086 (1995).
[CrossRef]

Kamli, A. A.

M. Siomau, A. A. Kamli, S. A. Moiseev, and B. C. Sanders, “Entanglement creation with negative index metamaterials,” Phys. Rev. A 85, 050303(R) (2012).
[CrossRef]

Kieling, K.

K. Lemr, a. Černoch, J. Soubusta, K. Kieling, J. Eisert, and M. Dušek, “Experimental implementation of the optimal linear-optical controlled phase gate,” Phys. Rev. Lett. 106, 013602 (2011).
[CrossRef]

K. Kieling, J. L. OBrien, and J. Eisert, “On photonic controlled phase gates,” New J. Phys. 12, 013003 (2010).
[CrossRef]

Kimble, H.

L.-M. Duan and H. Kimble, “Scalable photonic quantum computation through cavity-assisted interactions,” Phys. Rev. Lett. 92, 127902 (2004).
[CrossRef]

Kimble, H. J.

K. S. Choi, H. Deng, J. Laurat, and H. J. Kimble, “Mapping photonic entanglement into and out of a quantum memory,” Nature 452, 67–71 (2008).
[CrossRef]

Q. A. Turchette, C. J. Hood, W. Lange, H. Mabuchi, and H. J. Kimble, “Measurement of conditional phase shifts for quantum logic,” Phys. Rev. Lett. 75, 4710–4713 (1995).
[CrossRef]

Kippenberg, T.

T. Kippenberg, S. Spillane, and K. Vahala, “Kerr-nonlinearity optical parametric oscillation in an ultrahigh-Q toroid microcavity,” Phys. Rev. Lett. 93, 083904 (2004).
[CrossRef]

Knill, E.

E. Knill, “Bounds on the probability of success of postselected nonlinear sign shifts implemented with linear optics,” Phys. Rev. A 68, 064303 (2003).
[CrossRef]

E. Knill, R. Laflamme, and G. J. Milburn, “A scheme for efficient quantum computation with linear optics,” Nature 409, 46–52 (2001).
[CrossRef]

Koashi, M.

M. Koashi, T. Yamamoto, and N. Imoto, “Probabilistic manipulation of entangled photons,” Phys. Rev. A 63, 030301(R) (2001).
[CrossRef]

Kofler, J.

X.-s. Ma, S. Zotter, J. Kofler, T. Jennewein, and A. Zeilinger, “Experimental generation of single photons via active multiplexing,” Phys. Rev. A 83, 043814 (2011).
[CrossRef]

Kojima, K.

H. F. Hofmann, K. Kojima, S. Takeuchi, and K. Sasaki, “Optimized phase switching using a single-atom nonlinearity,” J. Opt. B 5, 218–221 (2003).
[CrossRef]

Kok, P.

P. Kok, K. Nemoto, T. C. Ralph, J. P. Dowling, and G. J. Milburn, “Linear optical quantum computing with photonic qubits,” Rev. Mod. Phys. 79, 135–174 (2007).
[CrossRef]

S. D. Barrett, P. Kok, K. Nemoto, R. G. Beausoleil, W. J. Munro, and T. P. Spiller, “Symmetry analyzer for nondestructive Bell-state detection using weak nonlinearities,” Phys. Rev. A 71, 060302(R) (2005).

P. Kok, H. Lee, and J. Dowling, “Single-photon quantum-nondemolition detectors constructed with linear optics and projective measurements,” Phys. Rev. A 66, 063814 (2002).
[CrossRef]

Korotkov, A. N.

M. Mariantoni, H. Wang, T. Yamamoto, M. Neeley, R. C. Bialczak, Y. Chen, M. Lenander, E. Lucero, A. D. OConnell, D. Sank, M. Weides, J. Wenner, Y. Yin, J. Zhao, A. N. Korotkov, A. N. Cleland, and J. M. Martinis, “Implementing the quantum von Neumann architecture with superconducting circuits,” Science 334, 61–65 (2011).
[CrossRef]

Kuang, L.-M.

X.-W. Wang, D.-Y. Zhang, S.-Q. Tang, L.-J. Xie, Z.-Y. Wang, and L.-M. Kuang, “Photonic two-qubit parity gate with tiny cross-Kerr nonlinearity,” Phys. Rev. A 85, 052326 (2012).
[CrossRef]

Kumar, P.

X. Li, P. Voss, J. Sharping, and P. Kumar, “Optical-fiber source of polarization-entangled photons in the 1550 nm telecom band,” Phys. Rev. Lett. 94, 053601 (2005).
[CrossRef]

Laflamme, R.

E. Knill, R. Laflamme, and G. J. Milburn, “A scheme for efficient quantum computation with linear optics,” Nature 409, 46–52 (2001).
[CrossRef]

Lancaster, G. P. T.

F. Schmidt-Kaler, H. Häffner, M. Riebe, S. Gulde, G. P. T. Lancaster, T. Deuschle, C. Becher, C. F. Roos, J. Eschner, and R. Blatt, “Realization of the Cirac–Zoller controlled-NOT quantum gate,” Nature 422, 408–411 (2003).
[CrossRef]

Lange, W.

Q. A. Turchette, C. J. Hood, W. Lange, H. Mabuchi, and H. J. Kimble, “Measurement of conditional phase shifts for quantum logic,” Phys. Rev. Lett. 75, 4710–4713 (1995).
[CrossRef]

Laurat, J.

K. S. Choi, H. Deng, J. Laurat, and H. J. Kimble, “Mapping photonic entanglement into and out of a quantum memory,” Nature 452, 67–71 (2008).
[CrossRef]

Lee, H.

P. Kok, H. Lee, and J. Dowling, “Single-photon quantum-nondemolition detectors constructed with linear optics and projective measurements,” Phys. Rev. A 66, 063814 (2002).
[CrossRef]

Lemr, K.

K. Lemr, a. Černoch, J. Soubusta, K. Kieling, J. Eisert, and M. Dušek, “Experimental implementation of the optimal linear-optical controlled phase gate,” Phys. Rev. Lett. 106, 013602 (2011).
[CrossRef]

Lenander, M.

M. Mariantoni, H. Wang, T. Yamamoto, M. Neeley, R. C. Bialczak, Y. Chen, M. Lenander, E. Lucero, A. D. OConnell, D. Sank, M. Weides, J. Wenner, Y. Yin, J. Zhao, A. N. Korotkov, A. N. Cleland, and J. M. Martinis, “Implementing the quantum von Neumann architecture with superconducting circuits,” Science 334, 61–65 (2011).
[CrossRef]

Levenson, J. A.

P. Grangier, J. A. Levenson, and J.-P. Poizat, “Quantum non-demolition measurements in optics,” Nature 396, 537–542 (1998).
[CrossRef]

Li, J.

Q. Lin and J. Li, “Quantum control gates with weak cross-Kerr nonlinearity,” Phys. Rev. A 79, 022301 (2009).
[CrossRef]

Li, K.

X. Zou, S. Zhang, K. Li, and G. Guo, “Linear optical implementation of the two-qubit controlled phase gate with conventional photon detectors,” Phys. Rev. A 75, 034302 (2007).
[CrossRef]

X. Zou, K. Li, and G. Guo, “Linear optical scheme for direct implementation of a nondestructive N-qubit controlled phase gate,” Phys. Rev. A 74, 044305 (2006).
[CrossRef]

Li, X.

X. Li, P. Voss, J. Sharping, and P. Kumar, “Optical-fiber source of polarization-entangled photons in the 1550 nm telecom band,” Phys. Rev. Lett. 94, 053601 (2005).
[CrossRef]

Lin, Q.

B. He, Q. Lin, and C. Simon, “Cross-Kerr nonlinearity between continuous-mode coherent states and single photons,” Phys. Rev. A 83, 053826 (2011).
[CrossRef]

Q. Lin and B. He, “Single-photon logic gates using minimal resources,” Phys. Rev. A 80, 042310 (2009).
[CrossRef]

Q. Lin and J. Li, “Quantum control gates with weak cross-Kerr nonlinearity,” Phys. Rev. A 79, 022301 (2009).
[CrossRef]

Lin, X.-M.

X.-M. Lin, Z.-W. Zhou, M.-Y. Ye, Y.-F. Xiao, and G.-C. Guo, “One-step implementation of a multiqubit controlled-phase-flip gate,” Phys. Rev. A 73, 012323 (2006).
[CrossRef]

Lloyd, S.

C. Weedbrook, S. Pirandola, R. Garca-Patrón, N. Cerf, T. Ralph, J. Shapiro, and S. Lloyd, “Gaussian quantum information,” Rev. Mod. Phys. 84, 621–669 (2012).
[CrossRef]

Lo, H.-Y.

H.-Y. Lo, P.-C. Su, and Y.-F. Chen, “Low-light-level cross-phase modulation by quantum interference,” Phys. Rev. A 81, 053829 (2010).
[CrossRef]

Long, G.-L.

Y.-B. Sheng, F.-G. Deng, and G.-L. Long, “Complete hyperentangled-Bell-state analysis for quantum communication,” Phys. Rev. A 82, 032318 (2010).
[CrossRef]

Louis, S. G. R.

S. G. R. Louis, W. J. Munro, T. P. Spiller, and K. Nemoto, “Loss in hybrid qubit-bus couplings and gates,” Phys. Rev. A 78, 022326 (2008).
[CrossRef]

Lu, C.-Y.

J.-W. Pan, Z.-B. Chen, C.-Y. Lu, H. Weinfurter, A. Zeilinger, and M. Zukowski, “Multiphoton entanglement and interferometry,” Rev. Mod. Phys. 84, 777–838 (2012).
[CrossRef]

Lu, P.-M.

Y. Xia, J. Song, P.-M. Lu, and H.-S. Song, “Efficient implementation of the two-qubit controlled phase gate with cross-Kerr nonlinearity,” J. Phys. B 44, 025503 (2011).
[CrossRef]

Y. Xia, J. Song, P.-M. Lu, and H.-S. Song, “Effective quantum teleportation of an atomic state between two cavities with the cross-Kerr nonlinearity by interference of polarized photons,” J. Appl. Phys. 109, 103111 (2011).
[CrossRef]

Lucero, E.

M. Mariantoni, H. Wang, T. Yamamoto, M. Neeley, R. C. Bialczak, Y. Chen, M. Lenander, E. Lucero, A. D. OConnell, D. Sank, M. Weides, J. Wenner, Y. Yin, J. Zhao, A. N. Korotkov, A. N. Cleland, and J. M. Martinis, “Implementing the quantum von Neumann architecture with superconducting circuits,” Science 334, 61–65 (2011).
[CrossRef]

Ma, X.-s.

X.-s. Ma, S. Zotter, N. Tetik, A. Qarry, T. Jennewein, and A. Zeilinger, “A high-speed tunable beam splitter for feed-forward photonic quantum information processing,” Opt. Express 19, 22723–22730 (2011).
[CrossRef]

X.-s. Ma, S. Zotter, J. Kofler, T. Jennewein, and A. Zeilinger, “Experimental generation of single photons via active multiplexing,” Phys. Rev. A 83, 043814 (2011).
[CrossRef]

Mabuchi, H.

Q. A. Turchette, C. J. Hood, W. Lange, H. Mabuchi, and H. J. Kimble, “Measurement of conditional phase shifts for quantum logic,” Phys. Rev. Lett. 75, 4710–4713 (1995).
[CrossRef]

Mariantoni, M.

M. Mariantoni, H. Wang, T. Yamamoto, M. Neeley, R. C. Bialczak, Y. Chen, M. Lenander, E. Lucero, A. D. OConnell, D. Sank, M. Weides, J. Wenner, Y. Yin, J. Zhao, A. N. Korotkov, A. N. Cleland, and J. M. Martinis, “Implementing the quantum von Neumann architecture with superconducting circuits,” Science 334, 61–65 (2011).
[CrossRef]

Martinis, J. M.

M. Mariantoni, H. Wang, T. Yamamoto, M. Neeley, R. C. Bialczak, Y. Chen, M. Lenander, E. Lucero, A. D. OConnell, D. Sank, M. Weides, J. Wenner, Y. Yin, J. Zhao, A. N. Korotkov, A. N. Cleland, and J. M. Martinis, “Implementing the quantum von Neumann architecture with superconducting circuits,” Science 334, 61–65 (2011).
[CrossRef]

Milburn, G. J.

P. Kok, K. Nemoto, T. C. Ralph, J. P. Dowling, and G. J. Milburn, “Linear optical quantum computing with photonic qubits,” Rev. Mod. Phys. 79, 135–174 (2007).
[CrossRef]

S. D. Barrett and G. J. Milburn, “Quantum-information processing via a lossy bus,” Phys. Rev. A 74, 060302(R) (2006).
[CrossRef]

E. Knill, R. Laflamme, and G. J. Milburn, “A scheme for efficient quantum computation with linear optics,” Nature 409, 46–52 (2001).
[CrossRef]

Moiseev, S. A.

M. Siomau, A. A. Kamli, S. A. Moiseev, and B. C. Sanders, “Entanglement creation with negative index metamaterials,” Phys. Rev. A 85, 050303(R) (2012).
[CrossRef]

Mølmer, K.

A. Sørensen and K. Mølmer, “Quantum computation with ions in thermal motion,” Phys. Rev. Lett. 82, 1971–1974 (1999).
[CrossRef]

Muller, R.

E. Nielsen, R. Muller, and M. Carroll, “Configuration interaction calculations of the controlled phase gate in double quantum dot qubits,” Phys. Rev. B 85, 035319 (2012).
[CrossRef]

Munro, W. J.

S. G. R. Louis, W. J. Munro, T. P. Spiller, and K. Nemoto, “Loss in hybrid qubit-bus couplings and gates,” Phys. Rev. A 78, 022326 (2008).
[CrossRef]

W. J. Munro, K. Nemoto, R. G. Beausoleil, and T. P. Spiller, “High-efficiency quantum-nondemolition single-photon-number-resolving detector,” Phys. Rev. A 71, 033819 (2005).
[CrossRef]

W. J. Munro, K. Nemoto, and T. P. Spiller, “Weak nonlinearities: a new route to optical quantum computation,” New J. Phys. 7, 137 (2005).
[CrossRef]

S. D. Barrett, P. Kok, K. Nemoto, R. G. Beausoleil, W. J. Munro, and T. P. Spiller, “Symmetry analyzer for nondestructive Bell-state detection using weak nonlinearities,” Phys. Rev. A 71, 060302(R) (2005).

K. Nemoto and W. J. Munro, “Nearly deterministic linear optical controlled-NOT gate,” Phys. Rev. Lett. 93, 250502 (2004).
[CrossRef]

Neeley, M.

M. Mariantoni, H. Wang, T. Yamamoto, M. Neeley, R. C. Bialczak, Y. Chen, M. Lenander, E. Lucero, A. D. OConnell, D. Sank, M. Weides, J. Wenner, Y. Yin, J. Zhao, A. N. Korotkov, A. N. Cleland, and J. M. Martinis, “Implementing the quantum von Neumann architecture with superconducting circuits,” Science 334, 61–65 (2011).
[CrossRef]

Nemoto, K.

S. G. R. Louis, W. J. Munro, T. P. Spiller, and K. Nemoto, “Loss in hybrid qubit-bus couplings and gates,” Phys. Rev. A 78, 022326 (2008).
[CrossRef]

P. Kok, K. Nemoto, T. C. Ralph, J. P. Dowling, and G. J. Milburn, “Linear optical quantum computing with photonic qubits,” Rev. Mod. Phys. 79, 135–174 (2007).
[CrossRef]

W. J. Munro, K. Nemoto, R. G. Beausoleil, and T. P. Spiller, “High-efficiency quantum-nondemolition single-photon-number-resolving detector,” Phys. Rev. A 71, 033819 (2005).
[CrossRef]

S. D. Barrett, P. Kok, K. Nemoto, R. G. Beausoleil, W. J. Munro, and T. P. Spiller, “Symmetry analyzer for nondestructive Bell-state detection using weak nonlinearities,” Phys. Rev. A 71, 060302(R) (2005).

W. J. Munro, K. Nemoto, and T. P. Spiller, “Weak nonlinearities: a new route to optical quantum computation,” New J. Phys. 7, 137 (2005).
[CrossRef]

K. Nemoto and W. J. Munro, “Nearly deterministic linear optical controlled-NOT gate,” Phys. Rev. Lett. 93, 250502 (2004).
[CrossRef]

Nielsen, E.

E. Nielsen, R. Muller, and M. Carroll, “Configuration interaction calculations of the controlled phase gate in double quantum dot qubits,” Phys. Rev. B 85, 035319 (2012).
[CrossRef]

Nielsen, M. A.

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

OBrien, J. L.

K. Kieling, J. L. OBrien, and J. Eisert, “On photonic controlled phase gates,” New J. Phys. 12, 013003 (2010).
[CrossRef]

OConnell, A. D.

M. Mariantoni, H. Wang, T. Yamamoto, M. Neeley, R. C. Bialczak, Y. Chen, M. Lenander, E. Lucero, A. D. OConnell, D. Sank, M. Weides, J. Wenner, Y. Yin, J. Zhao, A. N. Korotkov, A. N. Cleland, and J. M. Martinis, “Implementing the quantum von Neumann architecture with superconducting circuits,” Science 334, 61–65 (2011).
[CrossRef]

Pan, J.-W.

J.-W. Pan, Z.-B. Chen, C.-Y. Lu, H. Weinfurter, A. Zeilinger, and M. Zukowski, “Multiphoton entanglement and interferometry,” Rev. Mod. Phys. 84, 777–838 (2012).
[CrossRef]

X.-M. Jin, J.-G. Ren, B. Yang, Z.-H. Yi, F. Zhou, X.-F. Xu, S.-K. Wang, D. Yang, Y.-F. Hu, S. Jiang, T. Yang, H. Yin, K. Chen, C.-Z. Peng, and J.-W. Pan, “Experimental free-space quantum teleportation,” Nat. Photonics 4, 376–381 (2010).
[CrossRef]

Peng, C.-Z.

X.-M. Jin, J.-G. Ren, B. Yang, Z.-H. Yi, F. Zhou, X.-F. Xu, S.-K. Wang, D. Yang, Y.-F. Hu, S. Jiang, T. Yang, H. Yin, K. Chen, C.-Z. Peng, and J.-W. Pan, “Experimental free-space quantum teleportation,” Nat. Photonics 4, 376–381 (2010).
[CrossRef]

Petroff, P.

I. Fushman, D. Englund, A. Faraon, N. Stoltz, P. Petroff, and J. Vuckovic, “Controlled phase shifts with a single quantum dot,” Science 320, 769–772 (2008).
[CrossRef]

Phoenix, S.

S. Phoenix, “Wave-packet evolution in the damped oscillator,” Phys. Rev. A 41, 5132–5138 (1990).
[CrossRef]

Pirandola, S.

C. Weedbrook, S. Pirandola, R. Garca-Patrón, N. Cerf, T. Ralph, J. Shapiro, and S. Lloyd, “Gaussian quantum information,” Rev. Mod. Phys. 84, 621–669 (2012).
[CrossRef]

Pittman, T.

T. Pittman, B. Jacobs, and J. Franson, “Probabilistic quantum logic operations using polarizing beam splitters,” Phys. Rev. A 64, 062311 (2001).
[CrossRef]

Poizat, J.-P.

P. Grangier, J. A. Levenson, and J.-P. Poizat, “Quantum non-demolition measurements in optics,” Nature 396, 537–542 (1998).
[CrossRef]

Qarry, A.

Ralph, T.

C. Weedbrook, S. Pirandola, R. Garca-Patrón, N. Cerf, T. Ralph, J. Shapiro, and S. Lloyd, “Gaussian quantum information,” Rev. Mod. Phys. 84, 621–669 (2012).
[CrossRef]

Ralph, T. C.

P. Kok, K. Nemoto, T. C. Ralph, J. P. Dowling, and G. J. Milburn, “Linear optical quantum computing with photonic qubits,” Rev. Mod. Phys. 79, 135–174 (2007).
[CrossRef]

Razavi, M.

J. H. Shapiro and M. Razavi, “Continuous-time cross-phase modulation and quantum computation,” New J. Phys. 9, 16 (2007).
[CrossRef]

Ren, J.-G.

X.-M. Jin, J.-G. Ren, B. Yang, Z.-H. Yi, F. Zhou, X.-F. Xu, S.-K. Wang, D. Yang, Y.-F. Hu, S. Jiang, T. Yang, H. Yin, K. Chen, C.-Z. Peng, and J.-W. Pan, “Experimental free-space quantum teleportation,” Nat. Photonics 4, 376–381 (2010).
[CrossRef]

Ren, Y.

B. He, Y. Ren, and J. Bergou, “Creation of high-quality long-distance entanglement with flexible resources,” Phys. Rev. A 79, 052323 (2009).
[CrossRef]

B. He, J. Bergou, and Y. Ren, “Universal discriminator for completely unknown optical qubits,” Phys. Rev. A 76, 032301 (2007).
[CrossRef]

Ren, Y.-H.

B. He, Y.-H. Ren, and J. A. Bergou, “Universal entangler with photon pairs in arbitrary states,” J. Phys. B 43, 025502 (2010).
[CrossRef]

Riebe, M.

F. Schmidt-Kaler, H. Häffner, M. Riebe, S. Gulde, G. P. T. Lancaster, T. Deuschle, C. Becher, C. F. Roos, J. Eschner, and R. Blatt, “Realization of the Cirac–Zoller controlled-NOT quantum gate,” Nature 422, 408–411 (2003).
[CrossRef]

Roos, C. F.

F. Schmidt-Kaler, H. Häffner, M. Riebe, S. Gulde, G. P. T. Lancaster, T. Deuschle, C. Becher, C. F. Roos, J. Eschner, and R. Blatt, “Realization of the Cirac–Zoller controlled-NOT quantum gate,” Nature 422, 408–411 (2003).
[CrossRef]

Sanders, B. C.

M. Siomau, A. A. Kamli, S. A. Moiseev, and B. C. Sanders, “Entanglement creation with negative index metamaterials,” Phys. Rev. A 85, 050303(R) (2012).
[CrossRef]

Sank, D.

M. Mariantoni, H. Wang, T. Yamamoto, M. Neeley, R. C. Bialczak, Y. Chen, M. Lenander, E. Lucero, A. D. OConnell, D. Sank, M. Weides, J. Wenner, Y. Yin, J. Zhao, A. N. Korotkov, A. N. Cleland, and J. M. Martinis, “Implementing the quantum von Neumann architecture with superconducting circuits,” Science 334, 61–65 (2011).
[CrossRef]

Sasaki, K.

H. F. Hofmann, K. Kojima, S. Takeuchi, and K. Sasaki, “Optimized phase switching using a single-atom nonlinearity,” J. Opt. B 5, 218–221 (2003).
[CrossRef]

Schmidt-Kaler, F.

F. Schmidt-Kaler, H. Häffner, M. Riebe, S. Gulde, G. P. T. Lancaster, T. Deuschle, C. Becher, C. F. Roos, J. Eschner, and R. Blatt, “Realization of the Cirac–Zoller controlled-NOT quantum gate,” Nature 422, 408–411 (2003).
[CrossRef]

Scully, M. O.

M. O. Scully and M. S. Zubairy, Quantum Optics (Cambridge University, 1997).

Shao, X.-Q.

Q. Guo, J. Bai, L.-Y. Cheng, X.-Q. Shao, H.-F. Wang, and S. Zhang, “Simplified optical quantum-information processing via weak cross-Kerr nonlinearities,” Phys. Rev. A 83, 054303 (2011).
[CrossRef]

Shapiro, J.

C. Weedbrook, S. Pirandola, R. Garca-Patrón, N. Cerf, T. Ralph, J. Shapiro, and S. Lloyd, “Gaussian quantum information,” Rev. Mod. Phys. 84, 621–669 (2012).
[CrossRef]

J. Shapiro, “Single-photon Kerr nonlinearities do not help quantum computation,” Phys. Rev. A 73, 062305 (2006).
[CrossRef]

Shapiro, J. H.

J. H. Shapiro and M. Razavi, “Continuous-time cross-phase modulation and quantum computation,” New J. Phys. 9, 16 (2007).
[CrossRef]

Sharping, J.

X. Li, P. Voss, J. Sharping, and P. Kumar, “Optical-fiber source of polarization-entangled photons in the 1550 nm telecom band,” Phys. Rev. Lett. 94, 053601 (2005).
[CrossRef]

Sheng, Y.-B.

Y.-B. Sheng, L. Zhou, S.-M. Zhao, and B.-Y. Zheng, “Efficient single-photon-assisted entanglement concentration for partially entangled photon pairs,” Phys. Rev. A 85, 012307 (2012).
[CrossRef]

Y.-B. Sheng, L. Zhou, and S.-M. Zhao, “Efficient two-step entanglement concentration for arbitrary W states,” Phys. Rev. A 85, 042302 (2012).
[CrossRef]

Y.-B. Sheng, F.-G. Deng, and G.-L. Long, “Complete hyperentangled-Bell-state analysis for quantum communication,” Phys. Rev. A 82, 032318 (2010).
[CrossRef]

Y.-B. Sheng, F.-G. Deng, and H.-Y. Zhou, “Nonlocal entanglement concentration scheme for partially entangled multipartite systems with nonlinear optics,” Phys. Rev. A 77, 062325 (2008).
[CrossRef]

Simon, C.

B. He, Q. Lin, and C. Simon, “Cross-Kerr nonlinearity between continuous-mode coherent states and single photons,” Phys. Rev. A 83, 053826 (2011).
[CrossRef]

Simon, M. K.

M. K. Simon, Probability Distributions Involving Gaussian Random Variables, a Handbook for Engineers, Scientists and Mathematicians (Springer, 2006).

Siomau, M.

M. Siomau, A. A. Kamli, S. A. Moiseev, and B. C. Sanders, “Entanglement creation with negative index metamaterials,” Phys. Rev. A 85, 050303(R) (2012).
[CrossRef]

Song, H.-S.

Y. Xia, J. Song, P.-M. Lu, and H.-S. Song, “Effective quantum teleportation of an atomic state between two cavities with the cross-Kerr nonlinearity by interference of polarized photons,” J. Appl. Phys. 109, 103111 (2011).
[CrossRef]

Y. Xia, J. Song, P.-M. Lu, and H.-S. Song, “Efficient implementation of the two-qubit controlled phase gate with cross-Kerr nonlinearity,” J. Phys. B 44, 025503 (2011).
[CrossRef]

Song, J.

Y. Xia, J. Song, P.-M. Lu, and H.-S. Song, “Efficient implementation of the two-qubit controlled phase gate with cross-Kerr nonlinearity,” J. Phys. B 44, 025503 (2011).
[CrossRef]

Y. Xia, J. Song, P.-M. Lu, and H.-S. Song, “Effective quantum teleportation of an atomic state between two cavities with the cross-Kerr nonlinearity by interference of polarized photons,” J. Appl. Phys. 109, 103111 (2011).
[CrossRef]

Y. Xia, J. Song, Z.-B. Yang, and S.-B. Zheng, “Controlled implementation of two-photon controlled phase gate within a network,” Quantum Inf. Comput. 10, 0821–0828 (2010).

Sørensen, A.

A. Sørensen and K. Mølmer, “Quantum computation with ions in thermal motion,” Phys. Rev. Lett. 82, 1971–1974 (1999).
[CrossRef]

Soubusta, J.

K. Lemr, a. Černoch, J. Soubusta, K. Kieling, J. Eisert, and M. Dušek, “Experimental implementation of the optimal linear-optical controlled phase gate,” Phys. Rev. Lett. 106, 013602 (2011).
[CrossRef]

Spillane, S.

T. Kippenberg, S. Spillane, and K. Vahala, “Kerr-nonlinearity optical parametric oscillation in an ultrahigh-Q toroid microcavity,” Phys. Rev. Lett. 93, 083904 (2004).
[CrossRef]

Spiller, T. P.

S. G. R. Louis, W. J. Munro, T. P. Spiller, and K. Nemoto, “Loss in hybrid qubit-bus couplings and gates,” Phys. Rev. A 78, 022326 (2008).
[CrossRef]

W. J. Munro, K. Nemoto, R. G. Beausoleil, and T. P. Spiller, “High-efficiency quantum-nondemolition single-photon-number-resolving detector,” Phys. Rev. A 71, 033819 (2005).
[CrossRef]

W. J. Munro, K. Nemoto, and T. P. Spiller, “Weak nonlinearities: a new route to optical quantum computation,” New J. Phys. 7, 137 (2005).
[CrossRef]

S. D. Barrett, P. Kok, K. Nemoto, R. G. Beausoleil, W. J. Munro, and T. P. Spiller, “Symmetry analyzer for nondestructive Bell-state detection using weak nonlinearities,” Phys. Rev. A 71, 060302(R) (2005).

Steinberg, A. M.

A. Feizpour, X. Xing, and A. M. Steinberg, “Amplifying single-photon nonlinearity using weak measurements,” Phys. Rev. Lett. 107, 133603 (2011).
[CrossRef]

Stoltz, N.

I. Fushman, D. Englund, A. Faraon, N. Stoltz, P. Petroff, and J. Vuckovic, “Controlled phase shifts with a single quantum dot,” Science 320, 769–772 (2008).
[CrossRef]

Su, P.-C.

H.-Y. Lo, P.-C. Su, and Y.-F. Chen, “Low-light-level cross-phase modulation by quantum interference,” Phys. Rev. A 81, 053829 (2010).
[CrossRef]

Su, X. H.

L. You, X. X. Yi, and X. H. Su, “Quantum logic between atoms inside a high-Q optical cavity,” Phys. Rev. A 67, 032308 (2003).
[CrossRef]

X. X. Yi, X. H. Su, and L. You, “Conditional quantum phase gate between two 3-state atoms,” Phys. Rev. Lett. 90, 097902 (2003).
[CrossRef]

Takeuchi, S.

H. F. Hofmann, K. Kojima, S. Takeuchi, and K. Sasaki, “Optimized phase switching using a single-atom nonlinearity,” J. Opt. B 5, 218–221 (2003).
[CrossRef]

Tang, S.-Q.

X.-W. Wang, D.-Y. Zhang, S.-Q. Tang, and L.-J. Xie, “Nondestructive Greenberger–Horne–Zeilinger-state analyzer,” Quantum Inf. Process. 12, 1065–1075 (2013).
[CrossRef]

X.-W. Wang, D.-Y. Zhang, S.-Q. Tang, L.-J. Xie, Z.-Y. Wang, and L.-M. Kuang, “Photonic two-qubit parity gate with tiny cross-Kerr nonlinearity,” Phys. Rev. A 85, 052326 (2012).
[CrossRef]

Tetik, N.

Turchette, Q. A.

Q. A. Turchette, C. J. Hood, W. Lange, H. Mabuchi, and H. J. Kimble, “Measurement of conditional phase shifts for quantum logic,” Phys. Rev. Lett. 75, 4710–4713 (1995).
[CrossRef]

Ukai, R.

R. Ukai, S. Yokoyama, J.-i. Yoshikawa, P. van Loock, and A. Furusawa, “Demonstration of a controlled-phase gate for continuous-variable one-way quantum computation,” Phys. Rev. Lett. 107, 250501 (2011).
[CrossRef]

Vahala, K.

T. Kippenberg, S. Spillane, and K. Vahala, “Kerr-nonlinearity optical parametric oscillation in an ultrahigh-Q toroid microcavity,” Phys. Rev. Lett. 93, 083904 (2004).
[CrossRef]

van Loock, P.

R. Ukai, S. Yokoyama, J.-i. Yoshikawa, P. van Loock, and A. Furusawa, “Demonstration of a controlled-phase gate for continuous-variable one-way quantum computation,” Phys. Rev. Lett. 107, 250501 (2011).
[CrossRef]

Voss, P.

X. Li, P. Voss, J. Sharping, and P. Kumar, “Optical-fiber source of polarization-entangled photons in the 1550 nm telecom band,” Phys. Rev. Lett. 94, 053601 (2005).
[CrossRef]

Vuckovic, J.

I. Fushman, D. Englund, A. Faraon, N. Stoltz, P. Petroff, and J. Vuckovic, “Controlled phase shifts with a single quantum dot,” Science 320, 769–772 (2008).
[CrossRef]

Wang, C.

C. Wang, Y. Zhang, and G.-S. Jin, “Polarization-entanglement purification and concentration using cross-kerr nonlinearity,” Quantum Inf. Comput. 11, 0988–1002 (2011).

Wang, H.

M. Mariantoni, H. Wang, T. Yamamoto, M. Neeley, R. C. Bialczak, Y. Chen, M. Lenander, E. Lucero, A. D. OConnell, D. Sank, M. Weides, J. Wenner, Y. Yin, J. Zhao, A. N. Korotkov, A. N. Cleland, and J. M. Martinis, “Implementing the quantum von Neumann architecture with superconducting circuits,” Science 334, 61–65 (2011).
[CrossRef]

Wang, H.-F.

Q. Guo, J. Bai, L.-Y. Cheng, X.-Q. Shao, H.-F. Wang, and S. Zhang, “Simplified optical quantum-information processing via weak cross-Kerr nonlinearities,” Phys. Rev. A 83, 054303 (2011).
[CrossRef]

Wang, M.-F.

M.-F. Wang, N.-Q. Jiang, Q.-L. Jin, and Y.-Z. Zheng, “Continuous-variable controlled-Z gate using an atomic ensemble,” Phys. Rev. A 83, 062339 (2011).
[CrossRef]

Wang, S.-K.

X.-M. Jin, J.-G. Ren, B. Yang, Z.-H. Yi, F. Zhou, X.-F. Xu, S.-K. Wang, D. Yang, Y.-F. Hu, S. Jiang, T. Yang, H. Yin, K. Chen, C.-Z. Peng, and J.-W. Pan, “Experimental free-space quantum teleportation,” Nat. Photonics 4, 376–381 (2010).
[CrossRef]

Wang, X.-W.

X.-W. Wang, D.-Y. Zhang, S.-Q. Tang, and L.-J. Xie, “Nondestructive Greenberger–Horne–Zeilinger-state analyzer,” Quantum Inf. Process. 12, 1065–1075 (2013).
[CrossRef]

X.-W. Wang, D.-Y. Zhang, S.-Q. Tang, L.-J. Xie, Z.-Y. Wang, and L.-M. Kuang, “Photonic two-qubit parity gate with tiny cross-Kerr nonlinearity,” Phys. Rev. A 85, 052326 (2012).
[CrossRef]

Wang, Z.-Y.

X.-W. Wang, D.-Y. Zhang, S.-Q. Tang, L.-J. Xie, Z.-Y. Wang, and L.-M. Kuang, “Photonic two-qubit parity gate with tiny cross-Kerr nonlinearity,” Phys. Rev. A 85, 052326 (2012).
[CrossRef]

Weedbrook, C.

C. Weedbrook, S. Pirandola, R. Garca-Patrón, N. Cerf, T. Ralph, J. Shapiro, and S. Lloyd, “Gaussian quantum information,” Rev. Mod. Phys. 84, 621–669 (2012).
[CrossRef]

Weides, M.

M. Mariantoni, H. Wang, T. Yamamoto, M. Neeley, R. C. Bialczak, Y. Chen, M. Lenander, E. Lucero, A. D. OConnell, D. Sank, M. Weides, J. Wenner, Y. Yin, J. Zhao, A. N. Korotkov, A. N. Cleland, and J. M. Martinis, “Implementing the quantum von Neumann architecture with superconducting circuits,” Science 334, 61–65 (2011).
[CrossRef]

Weinfurter, H.

J.-W. Pan, Z.-B. Chen, C.-Y. Lu, H. Weinfurter, A. Zeilinger, and M. Zukowski, “Multiphoton entanglement and interferometry,” Rev. Mod. Phys. 84, 777–838 (2012).
[CrossRef]

Wenner, J.

M. Mariantoni, H. Wang, T. Yamamoto, M. Neeley, R. C. Bialczak, Y. Chen, M. Lenander, E. Lucero, A. D. OConnell, D. Sank, M. Weides, J. Wenner, Y. Yin, J. Zhao, A. N. Korotkov, A. N. Cleland, and J. M. Martinis, “Implementing the quantum von Neumann architecture with superconducting circuits,” Science 334, 61–65 (2011).
[CrossRef]

Xia, Y.

Y. Xia, J. Song, P.-M. Lu, and H.-S. Song, “Efficient implementation of the two-qubit controlled phase gate with cross-Kerr nonlinearity,” J. Phys. B 44, 025503 (2011).
[CrossRef]

Y. Xia, J. Song, P.-M. Lu, and H.-S. Song, “Effective quantum teleportation of an atomic state between two cavities with the cross-Kerr nonlinearity by interference of polarized photons,” J. Appl. Phys. 109, 103111 (2011).
[CrossRef]

Y. Xia, J. Song, Z.-B. Yang, and S.-B. Zheng, “Controlled implementation of two-photon controlled phase gate within a network,” Quantum Inf. Comput. 10, 0821–0828 (2010).

Xiao, Y.-F.

Y.-F. Xiao, X.-B. Zou, and G.-C. Guo, “One-step implementation of an N-qubit controlled-phase gate with neutral atoms trapped in an optical cavity,” Phys. Rev. A 75, 054303 (2007).
[CrossRef]

X.-M. Lin, Z.-W. Zhou, M.-Y. Ye, Y.-F. Xiao, and G.-C. Guo, “One-step implementation of a multiqubit controlled-phase-flip gate,” Phys. Rev. A 73, 012323 (2006).
[CrossRef]

Xie, L.-J.

X.-W. Wang, D.-Y. Zhang, S.-Q. Tang, and L.-J. Xie, “Nondestructive Greenberger–Horne–Zeilinger-state analyzer,” Quantum Inf. Process. 12, 1065–1075 (2013).
[CrossRef]

X.-W. Wang, D.-Y. Zhang, S.-Q. Tang, L.-J. Xie, Z.-Y. Wang, and L.-M. Kuang, “Photonic two-qubit parity gate with tiny cross-Kerr nonlinearity,” Phys. Rev. A 85, 052326 (2012).
[CrossRef]

Xing, X.

A. Feizpour, X. Xing, and A. M. Steinberg, “Amplifying single-photon nonlinearity using weak measurements,” Phys. Rev. Lett. 107, 133603 (2011).
[CrossRef]

Xiong, W.

Xiu, X.-M.

X.-M. Xiu, L. Dong, Y.-J. Gao, and X. X. Yi, “Nearly deterministic controlled-not gate with weak cross-Kerr nonlinearities,” Quantum Inf. Comput. 12, 0159–0170 (2012).

Xu, X.-F.

X.-M. Jin, J.-G. Ren, B. Yang, Z.-H. Yi, F. Zhou, X.-F. Xu, S.-K. Wang, D. Yang, Y.-F. Hu, S. Jiang, T. Yang, H. Yin, K. Chen, C.-Z. Peng, and J.-W. Pan, “Experimental free-space quantum teleportation,” Nat. Photonics 4, 376–381 (2010).
[CrossRef]

Yamamoto, T.

M. Mariantoni, H. Wang, T. Yamamoto, M. Neeley, R. C. Bialczak, Y. Chen, M. Lenander, E. Lucero, A. D. OConnell, D. Sank, M. Weides, J. Wenner, Y. Yin, J. Zhao, A. N. Korotkov, A. N. Cleland, and J. M. Martinis, “Implementing the quantum von Neumann architecture with superconducting circuits,” Science 334, 61–65 (2011).
[CrossRef]

M. Koashi, T. Yamamoto, and N. Imoto, “Probabilistic manipulation of entangled photons,” Phys. Rev. A 63, 030301(R) (2001).
[CrossRef]

Yamamoto, Y.

I. Chuang and Y. Yamamoto, “Simple quantum computer,” Phys. Rev. A 52, 3489–3496 (1995).
[CrossRef]

Yang, B.

X.-M. Jin, J.-G. Ren, B. Yang, Z.-H. Yi, F. Zhou, X.-F. Xu, S.-K. Wang, D. Yang, Y.-F. Hu, S. Jiang, T. Yang, H. Yin, K. Chen, C.-Z. Peng, and J.-W. Pan, “Experimental free-space quantum teleportation,” Nat. Photonics 4, 376–381 (2010).
[CrossRef]

Yang, D.

X.-M. Jin, J.-G. Ren, B. Yang, Z.-H. Yi, F. Zhou, X.-F. Xu, S.-K. Wang, D. Yang, Y.-F. Hu, S. Jiang, T. Yang, H. Yin, K. Chen, C.-Z. Peng, and J.-W. Pan, “Experimental free-space quantum teleportation,” Nat. Photonics 4, 376–381 (2010).
[CrossRef]

Yang, T.

X.-M. Jin, J.-G. Ren, B. Yang, Z.-H. Yi, F. Zhou, X.-F. Xu, S.-K. Wang, D. Yang, Y.-F. Hu, S. Jiang, T. Yang, H. Yin, K. Chen, C.-Z. Peng, and J.-W. Pan, “Experimental free-space quantum teleportation,” Nat. Photonics 4, 376–381 (2010).
[CrossRef]

Yang, Z.-B.

Y. Xia, J. Song, Z.-B. Yang, and S.-B. Zheng, “Controlled implementation of two-photon controlled phase gate within a network,” Quantum Inf. Comput. 10, 0821–0828 (2010).

Ye, L.

Ye, M.-Y.

X.-M. Lin, Z.-W. Zhou, M.-Y. Ye, Y.-F. Xiao, and G.-C. Guo, “One-step implementation of a multiqubit controlled-phase-flip gate,” Phys. Rev. A 73, 012323 (2006).
[CrossRef]

Yeon, K. H.

Yi, X. X.

X.-M. Xiu, L. Dong, Y.-J. Gao, and X. X. Yi, “Nearly deterministic controlled-not gate with weak cross-Kerr nonlinearities,” Quantum Inf. Comput. 12, 0159–0170 (2012).

X. X. Yi, X. H. Su, and L. You, “Conditional quantum phase gate between two 3-state atoms,” Phys. Rev. Lett. 90, 097902 (2003).
[CrossRef]

L. You, X. X. Yi, and X. H. Su, “Quantum logic between atoms inside a high-Q optical cavity,” Phys. Rev. A 67, 032308 (2003).
[CrossRef]

Yi, Z.-H.

X.-M. Jin, J.-G. Ren, B. Yang, Z.-H. Yi, F. Zhou, X.-F. Xu, S.-K. Wang, D. Yang, Y.-F. Hu, S. Jiang, T. Yang, H. Yin, K. Chen, C.-Z. Peng, and J.-W. Pan, “Experimental free-space quantum teleportation,” Nat. Photonics 4, 376–381 (2010).
[CrossRef]

Yin, G.

D. Braje, V. Balić, G. Yin, and S. Harris, “Low-light-level nonlinear optics with slow light,” Phys. Rev. A 68, 041801(R) (2003).
[CrossRef]

Yin, H.

X.-M. Jin, J.-G. Ren, B. Yang, Z.-H. Yi, F. Zhou, X.-F. Xu, S.-K. Wang, D. Yang, Y.-F. Hu, S. Jiang, T. Yang, H. Yin, K. Chen, C.-Z. Peng, and J.-W. Pan, “Experimental free-space quantum teleportation,” Nat. Photonics 4, 376–381 (2010).
[CrossRef]

Yin, Y.

M. Mariantoni, H. Wang, T. Yamamoto, M. Neeley, R. C. Bialczak, Y. Chen, M. Lenander, E. Lucero, A. D. OConnell, D. Sank, M. Weides, J. Wenner, Y. Yin, J. Zhao, A. N. Korotkov, A. N. Cleland, and J. M. Martinis, “Implementing the quantum von Neumann architecture with superconducting circuits,” Science 334, 61–65 (2011).
[CrossRef]

Yokoyama, S.

R. Ukai, S. Yokoyama, J.-i. Yoshikawa, P. van Loock, and A. Furusawa, “Demonstration of a controlled-phase gate for continuous-variable one-way quantum computation,” Phys. Rev. Lett. 107, 250501 (2011).
[CrossRef]

Yoshikawa, J.-i.

R. Ukai, S. Yokoyama, J.-i. Yoshikawa, P. van Loock, and A. Furusawa, “Demonstration of a controlled-phase gate for continuous-variable one-way quantum computation,” Phys. Rev. Lett. 107, 250501 (2011).
[CrossRef]

You, L.

L. You, X. X. Yi, and X. H. Su, “Quantum logic between atoms inside a high-Q optical cavity,” Phys. Rev. A 67, 032308 (2003).
[CrossRef]

X. X. Yi, X. H. Su, and L. You, “Conditional quantum phase gate between two 3-state atoms,” Phys. Rev. Lett. 90, 097902 (2003).
[CrossRef]

Yu, S. C.

Zeilinger, A.

J.-W. Pan, Z.-B. Chen, C.-Y. Lu, H. Weinfurter, A. Zeilinger, and M. Zukowski, “Multiphoton entanglement and interferometry,” Rev. Mod. Phys. 84, 777–838 (2012).
[CrossRef]

X.-s. Ma, S. Zotter, N. Tetik, A. Qarry, T. Jennewein, and A. Zeilinger, “A high-speed tunable beam splitter for feed-forward photonic quantum information processing,” Opt. Express 19, 22723–22730 (2011).
[CrossRef]

X.-s. Ma, S. Zotter, J. Kofler, T. Jennewein, and A. Zeilinger, “Experimental generation of single photons via active multiplexing,” Phys. Rev. A 83, 043814 (2011).
[CrossRef]

Zhang, D.-Y.

X.-W. Wang, D.-Y. Zhang, S.-Q. Tang, and L.-J. Xie, “Nondestructive Greenberger–Horne–Zeilinger-state analyzer,” Quantum Inf. Process. 12, 1065–1075 (2013).
[CrossRef]

X.-W. Wang, D.-Y. Zhang, S.-Q. Tang, L.-J. Xie, Z.-Y. Wang, and L.-M. Kuang, “Photonic two-qubit parity gate with tiny cross-Kerr nonlinearity,” Phys. Rev. A 85, 052326 (2012).
[CrossRef]

Zhang, S.

Y. Q. Zhang, S. Zhang, K. H. Yeon, and S. C. Yu, “One-step implementation of a multiqubit controlled-phase gate with superconducting quantum interference devices coupled to a resonator,” J. Opt. Soc. Am. B 29, 300–304 (2012).
[CrossRef]

Q. Guo, J. Bai, L.-Y. Cheng, X.-Q. Shao, H.-F. Wang, and S. Zhang, “Simplified optical quantum-information processing via weak cross-Kerr nonlinearities,” Phys. Rev. A 83, 054303 (2011).
[CrossRef]

X. Zou, S. Zhang, K. Li, and G. Guo, “Linear optical implementation of the two-qubit controlled phase gate with conventional photon detectors,” Phys. Rev. A 75, 034302 (2007).
[CrossRef]

Zhang, Y.

C. Wang, Y. Zhang, and G.-S. Jin, “Polarization-entanglement purification and concentration using cross-kerr nonlinearity,” Quantum Inf. Comput. 11, 0988–1002 (2011).

Zhang, Y. Q.

Zhao, J.

M. Mariantoni, H. Wang, T. Yamamoto, M. Neeley, R. C. Bialczak, Y. Chen, M. Lenander, E. Lucero, A. D. OConnell, D. Sank, M. Weides, J. Wenner, Y. Yin, J. Zhao, A. N. Korotkov, A. N. Cleland, and J. M. Martinis, “Implementing the quantum von Neumann architecture with superconducting circuits,” Science 334, 61–65 (2011).
[CrossRef]

Zhao, S.-M.

Y.-B. Sheng, L. Zhou, S.-M. Zhao, and B.-Y. Zheng, “Efficient single-photon-assisted entanglement concentration for partially entangled photon pairs,” Phys. Rev. A 85, 012307 (2012).
[CrossRef]

Y.-B. Sheng, L. Zhou, and S.-M. Zhao, “Efficient two-step entanglement concentration for arbitrary W states,” Phys. Rev. A 85, 042302 (2012).
[CrossRef]

Zheng, B.-Y.

Y.-B. Sheng, L. Zhou, S.-M. Zhao, and B.-Y. Zheng, “Efficient single-photon-assisted entanglement concentration for partially entangled photon pairs,” Phys. Rev. A 85, 012307 (2012).
[CrossRef]

Zheng, S.-B.

Y. Xia, J. Song, Z.-B. Yang, and S.-B. Zheng, “Controlled implementation of two-photon controlled phase gate within a network,” Quantum Inf. Comput. 10, 0821–0828 (2010).

Zheng, Y.-Z.

M.-F. Wang, N.-Q. Jiang, Q.-L. Jin, and Y.-Z. Zheng, “Continuous-variable controlled-Z gate using an atomic ensemble,” Phys. Rev. A 83, 062339 (2011).
[CrossRef]

Zhou, F.

X.-M. Jin, J.-G. Ren, B. Yang, Z.-H. Yi, F. Zhou, X.-F. Xu, S.-K. Wang, D. Yang, Y.-F. Hu, S. Jiang, T. Yang, H. Yin, K. Chen, C.-Z. Peng, and J.-W. Pan, “Experimental free-space quantum teleportation,” Nat. Photonics 4, 376–381 (2010).
[CrossRef]

Zhou, H.-Y.

Y.-B. Sheng, F.-G. Deng, and H.-Y. Zhou, “Nonlocal entanglement concentration scheme for partially entangled multipartite systems with nonlinear optics,” Phys. Rev. A 77, 062325 (2008).
[CrossRef]

Zhou, L.

Y.-B. Sheng, L. Zhou, and S.-M. Zhao, “Efficient two-step entanglement concentration for arbitrary W states,” Phys. Rev. A 85, 042302 (2012).
[CrossRef]

Y.-B. Sheng, L. Zhou, S.-M. Zhao, and B.-Y. Zheng, “Efficient single-photon-assisted entanglement concentration for partially entangled photon pairs,” Phys. Rev. A 85, 012307 (2012).
[CrossRef]

Zhou, Z.-W.

X.-M. Lin, Z.-W. Zhou, M.-Y. Ye, Y.-F. Xiao, and G.-C. Guo, “One-step implementation of a multiqubit controlled-phase-flip gate,” Phys. Rev. A 73, 012323 (2006).
[CrossRef]

Zoller, P.

J. Cirac and P. Zoller, “Quantum computations with cold trapped ions,” Phys. Rev. Lett. 74, 4091–4094 (1995).
[CrossRef]

C. W. Gardiner and P. Zoller, Quantum Noise (Springer, 2000).

Zotter, S.

X.-s. Ma, S. Zotter, J. Kofler, T. Jennewein, and A. Zeilinger, “Experimental generation of single photons via active multiplexing,” Phys. Rev. A 83, 043814 (2011).
[CrossRef]

X.-s. Ma, S. Zotter, N. Tetik, A. Qarry, T. Jennewein, and A. Zeilinger, “A high-speed tunable beam splitter for feed-forward photonic quantum information processing,” Opt. Express 19, 22723–22730 (2011).
[CrossRef]

Zou, X.

X. Zou, S. Zhang, K. Li, and G. Guo, “Linear optical implementation of the two-qubit controlled phase gate with conventional photon detectors,” Phys. Rev. A 75, 034302 (2007).
[CrossRef]

X. Zou, K. Li, and G. Guo, “Linear optical scheme for direct implementation of a nondestructive N-qubit controlled phase gate,” Phys. Rev. A 74, 044305 (2006).
[CrossRef]

Zou, X.-B.

Y.-F. Xiao, X.-B. Zou, and G.-C. Guo, “One-step implementation of an N-qubit controlled-phase gate with neutral atoms trapped in an optical cavity,” Phys. Rev. A 75, 054303 (2007).
[CrossRef]

Zubairy, M. S.

M. O. Scully and M. S. Zubairy, Quantum Optics (Cambridge University, 1997).

Zukowski, M.

J.-W. Pan, Z.-B. Chen, C.-Y. Lu, H. Weinfurter, A. Zeilinger, and M. Zukowski, “Multiphoton entanglement and interferometry,” Rev. Mod. Phys. 84, 777–838 (2012).
[CrossRef]

J. Appl. Phys.

Y. Xia, J. Song, P.-M. Lu, and H.-S. Song, “Effective quantum teleportation of an atomic state between two cavities with the cross-Kerr nonlinearity by interference of polarized photons,” J. Appl. Phys. 109, 103111 (2011).
[CrossRef]

J. Opt. B

H. F. Hofmann, K. Kojima, S. Takeuchi, and K. Sasaki, “Optimized phase switching using a single-atom nonlinearity,” J. Opt. B 5, 218–221 (2003).
[CrossRef]

J. Opt. Soc. Am. B

J. Phys. B

Y. Xia, J. Song, P.-M. Lu, and H.-S. Song, “Efficient implementation of the two-qubit controlled phase gate with cross-Kerr nonlinearity,” J. Phys. B 44, 025503 (2011).
[CrossRef]

B. He, Y.-H. Ren, and J. A. Bergou, “Universal entangler with photon pairs in arbitrary states,” J. Phys. B 43, 025502 (2010).
[CrossRef]

Nat. Photonics

X.-M. Jin, J.-G. Ren, B. Yang, Z.-H. Yi, F. Zhou, X.-F. Xu, S.-K. Wang, D. Yang, Y.-F. Hu, S. Jiang, T. Yang, H. Yin, K. Chen, C.-Z. Peng, and J.-W. Pan, “Experimental free-space quantum teleportation,” Nat. Photonics 4, 376–381 (2010).
[CrossRef]

Nature

P. Grangier, J. A. Levenson, and J.-P. Poizat, “Quantum non-demolition measurements in optics,” Nature 396, 537–542 (1998).
[CrossRef]

E. Knill, R. Laflamme, and G. J. Milburn, “A scheme for efficient quantum computation with linear optics,” Nature 409, 46–52 (2001).
[CrossRef]

K. S. Choi, H. Deng, J. Laurat, and H. J. Kimble, “Mapping photonic entanglement into and out of a quantum memory,” Nature 452, 67–71 (2008).
[CrossRef]

F. Schmidt-Kaler, H. Häffner, M. Riebe, S. Gulde, G. P. T. Lancaster, T. Deuschle, C. Becher, C. F. Roos, J. Eschner, and R. Blatt, “Realization of the Cirac–Zoller controlled-NOT quantum gate,” Nature 422, 408–411 (2003).
[CrossRef]

New J. Phys.

K. Kieling, J. L. OBrien, and J. Eisert, “On photonic controlled phase gates,” New J. Phys. 12, 013003 (2010).
[CrossRef]

J. H. Shapiro and M. Razavi, “Continuous-time cross-phase modulation and quantum computation,” New J. Phys. 9, 16 (2007).
[CrossRef]

W. J. Munro, K. Nemoto, and T. P. Spiller, “Weak nonlinearities: a new route to optical quantum computation,” New J. Phys. 7, 137 (2005).
[CrossRef]

Opt. Express

Phys. Lett. A

C. C. Gerry and T. Bui, “Quantum non-demolition measurement of photon number using weak nonlinearities,” Phys. Lett. A 372, 7101–7104 (2008).
[CrossRef]

Phys. Rev. A

X.-s. Ma, S. Zotter, J. Kofler, T. Jennewein, and A. Zeilinger, “Experimental generation of single photons via active multiplexing,” Phys. Rev. A 83, 043814 (2011).
[CrossRef]

B. He, Q. Lin, and C. Simon, “Cross-Kerr nonlinearity between continuous-mode coherent states and single photons,” Phys. Rev. A 83, 053826 (2011).
[CrossRef]

S. Phoenix, “Wave-packet evolution in the damped oscillator,” Phys. Rev. A 41, 5132–5138 (1990).
[CrossRef]

H. Jeong, “Quantum computation using weak nonlinearities: robustness against decoherence,” Phys. Rev. A 73, 052320 (2006).
[CrossRef]

S. G. R. Louis, W. J. Munro, T. P. Spiller, and K. Nemoto, “Loss in hybrid qubit-bus couplings and gates,” Phys. Rev. A 78, 022326 (2008).
[CrossRef]

P. Kok, H. Lee, and J. Dowling, “Single-photon quantum-nondemolition detectors constructed with linear optics and projective measurements,” Phys. Rev. A 66, 063814 (2002).
[CrossRef]

H.-Y. Lo, P.-C. Su, and Y.-F. Chen, “Low-light-level cross-phase modulation by quantum interference,” Phys. Rev. A 81, 053829 (2010).
[CrossRef]

J. Gea-Banacloche, “Impossibility of large phase shifts via the giant Kerr effect with single-photon wave packets,” Phys. Rev. A 81, 043823 (2010).
[CrossRef]

J. Shapiro, “Single-photon Kerr nonlinearities do not help quantum computation,” Phys. Rev. A 73, 062305 (2006).
[CrossRef]

S. D. Barrett and G. J. Milburn, “Quantum-information processing via a lossy bus,” Phys. Rev. A 74, 060302(R) (2006).
[CrossRef]

B. He, J. Bergou, and Y. Ren, “Universal discriminator for completely unknown optical qubits,” Phys. Rev. A 76, 032301 (2007).
[CrossRef]

Y.-B. Sheng, F.-G. Deng, and H.-Y. Zhou, “Nonlocal entanglement concentration scheme for partially entangled multipartite systems with nonlinear optics,” Phys. Rev. A 77, 062325 (2008).
[CrossRef]

Q. Lin and B. He, “Single-photon logic gates using minimal resources,” Phys. Rev. A 80, 042310 (2009).
[CrossRef]

B. He, Y. Ren, and J. Bergou, “Creation of high-quality long-distance entanglement with flexible resources,” Phys. Rev. A 79, 052323 (2009).
[CrossRef]

Y.-B. Sheng, F.-G. Deng, and G.-L. Long, “Complete hyperentangled-Bell-state analysis for quantum communication,” Phys. Rev. A 82, 032318 (2010).
[CrossRef]

S. D. Barrett, P. Kok, K. Nemoto, R. G. Beausoleil, W. J. Munro, and T. P. Spiller, “Symmetry analyzer for nondestructive Bell-state detection using weak nonlinearities,” Phys. Rev. A 71, 060302(R) (2005).

Q. Guo, J. Bai, L.-Y. Cheng, X.-Q. Shao, H.-F. Wang, and S. Zhang, “Simplified optical quantum-information processing via weak cross-Kerr nonlinearities,” Phys. Rev. A 83, 054303 (2011).
[CrossRef]

F.-G. Deng, “Efficient multipartite entanglement purification with the entanglement link from a subspace,” Phys. Rev. A 84, 052312 (2011).
[CrossRef]

Y.-B. Sheng, L. Zhou, S.-M. Zhao, and B.-Y. Zheng, “Efficient single-photon-assisted entanglement concentration for partially entangled photon pairs,” Phys. Rev. A 85, 012307 (2012).
[CrossRef]

Y.-B. Sheng, L. Zhou, and S.-M. Zhao, “Efficient two-step entanglement concentration for arbitrary W states,” Phys. Rev. A 85, 042302 (2012).
[CrossRef]

X.-W. Wang, D.-Y. Zhang, S.-Q. Tang, L.-J. Xie, Z.-Y. Wang, and L.-M. Kuang, “Photonic two-qubit parity gate with tiny cross-Kerr nonlinearity,” Phys. Rev. A 85, 052326 (2012).
[CrossRef]

D. Braje, V. Balić, G. Yin, and S. Harris, “Low-light-level nonlinear optics with slow light,” Phys. Rev. A 68, 041801(R) (2003).
[CrossRef]

W. J. Munro, K. Nemoto, R. G. Beausoleil, and T. P. Spiller, “High-efficiency quantum-nondemolition single-photon-number-resolving detector,” Phys. Rev. A 71, 033819 (2005).
[CrossRef]

E. Knill, “Bounds on the probability of success of postselected nonlinear sign shifts implemented with linear optics,” Phys. Rev. A 68, 064303 (2003).
[CrossRef]

Q. Lin and J. Li, “Quantum control gates with weak cross-Kerr nonlinearity,” Phys. Rev. A 79, 022301 (2009).
[CrossRef]

M.-F. Wang, N.-Q. Jiang, Q.-L. Jin, and Y.-Z. Zheng, “Continuous-variable controlled-Z gate using an atomic ensemble,” Phys. Rev. A 83, 062339 (2011).
[CrossRef]

L. You, X. X. Yi, and X. H. Su, “Quantum logic between atoms inside a high-Q optical cavity,” Phys. Rev. A 67, 032308 (2003).
[CrossRef]

X.-M. Lin, Z.-W. Zhou, M.-Y. Ye, Y.-F. Xiao, and G.-C. Guo, “One-step implementation of a multiqubit controlled-phase-flip gate,” Phys. Rev. A 73, 012323 (2006).
[CrossRef]

X. Zou, S. Zhang, K. Li, and G. Guo, “Linear optical implementation of the two-qubit controlled phase gate with conventional photon detectors,” Phys. Rev. A 75, 034302 (2007).
[CrossRef]

X. Zou, K. Li, and G. Guo, “Linear optical scheme for direct implementation of a nondestructive N-qubit controlled phase gate,” Phys. Rev. A 74, 044305 (2006).
[CrossRef]

Y.-F. Xiao, X.-B. Zou, and G.-C. Guo, “One-step implementation of an N-qubit controlled-phase gate with neutral atoms trapped in an optical cavity,” Phys. Rev. A 75, 054303 (2007).
[CrossRef]

I. Chuang and Y. Yamamoto, “Simple quantum computer,” Phys. Rev. A 52, 3489–3496 (1995).
[CrossRef]

M. Koashi, T. Yamamoto, and N. Imoto, “Probabilistic manipulation of entangled photons,” Phys. Rev. A 63, 030301(R) (2001).
[CrossRef]

T. Pittman, B. Jacobs, and J. Franson, “Probabilistic quantum logic operations using polarizing beam splitters,” Phys. Rev. A 64, 062311 (2001).
[CrossRef]

M. Siomau, A. A. Kamli, S. A. Moiseev, and B. C. Sanders, “Entanglement creation with negative index metamaterials,” Phys. Rev. A 85, 050303(R) (2012).
[CrossRef]

Phys. Rev. B

E. Nielsen, R. Muller, and M. Carroll, “Configuration interaction calculations of the controlled phase gate in double quantum dot qubits,” Phys. Rev. B 85, 035319 (2012).
[CrossRef]

Phys. Rev. Lett.

R. Ukai, S. Yokoyama, J.-i. Yoshikawa, P. van Loock, and A. Furusawa, “Demonstration of a controlled-phase gate for continuous-variable one-way quantum computation,” Phys. Rev. Lett. 107, 250501 (2011).
[CrossRef]

K. Lemr, a. Černoch, J. Soubusta, K. Kieling, J. Eisert, and M. Dušek, “Experimental implementation of the optimal linear-optical controlled phase gate,” Phys. Rev. Lett. 106, 013602 (2011).
[CrossRef]

K. Nemoto and W. J. Munro, “Nearly deterministic linear optical controlled-NOT gate,” Phys. Rev. Lett. 93, 250502 (2004).
[CrossRef]

A. Sørensen and K. Mølmer, “Quantum computation with ions in thermal motion,” Phys. Rev. Lett. 82, 1971–1974 (1999).
[CrossRef]

A. Barenco, D. Deutsch, A. Ekert, and R. Jozsa, “Conditional quantum dynamics and logic gates,” Phys. Rev. Lett. 74, 4083–4086 (1995).
[CrossRef]

J. Cirac and P. Zoller, “Quantum computations with cold trapped ions,” Phys. Rev. Lett. 74, 4091–4094 (1995).
[CrossRef]

X. X. Yi, X. H. Su, and L. You, “Conditional quantum phase gate between two 3-state atoms,” Phys. Rev. Lett. 90, 097902 (2003).
[CrossRef]

L.-M. Duan and H. Kimble, “Scalable photonic quantum computation through cavity-assisted interactions,” Phys. Rev. Lett. 92, 127902 (2004).
[CrossRef]

Q. A. Turchette, C. J. Hood, W. Lange, H. Mabuchi, and H. J. Kimble, “Measurement of conditional phase shifts for quantum logic,” Phys. Rev. Lett. 75, 4710–4713 (1995).
[CrossRef]

T. Kippenberg, S. Spillane, and K. Vahala, “Kerr-nonlinearity optical parametric oscillation in an ultrahigh-Q toroid microcavity,” Phys. Rev. Lett. 93, 083904 (2004).
[CrossRef]

X. Li, P. Voss, J. Sharping, and P. Kumar, “Optical-fiber source of polarization-entangled photons in the 1550 nm telecom band,” Phys. Rev. Lett. 94, 053601 (2005).
[CrossRef]

S. Harris and L. Hau, “Nonlinear optics at low light levels,” Phys. Rev. Lett. 82, 4611–4614 (1999).
[CrossRef]

A. Feizpour, X. Xing, and A. M. Steinberg, “Amplifying single-photon nonlinearity using weak measurements,” Phys. Rev. Lett. 107, 133603 (2011).
[CrossRef]

Quantum Inf. Comput.

C. Wang, Y. Zhang, and G.-S. Jin, “Polarization-entanglement purification and concentration using cross-kerr nonlinearity,” Quantum Inf. Comput. 11, 0988–1002 (2011).

Y. Xia, J. Song, Z.-B. Yang, and S.-B. Zheng, “Controlled implementation of two-photon controlled phase gate within a network,” Quantum Inf. Comput. 10, 0821–0828 (2010).

X.-M. Xiu, L. Dong, Y.-J. Gao, and X. X. Yi, “Nearly deterministic controlled-not gate with weak cross-Kerr nonlinearities,” Quantum Inf. Comput. 12, 0159–0170 (2012).

Quantum Inf. Process.

X.-W. Wang, D.-Y. Zhang, S.-Q. Tang, and L.-J. Xie, “Nondestructive Greenberger–Horne–Zeilinger-state analyzer,” Quantum Inf. Process. 12, 1065–1075 (2013).
[CrossRef]

Rev. Mod. Phys.

C. Weedbrook, S. Pirandola, R. Garca-Patrón, N. Cerf, T. Ralph, J. Shapiro, and S. Lloyd, “Gaussian quantum information,” Rev. Mod. Phys. 84, 621–669 (2012).
[CrossRef]

P. Kok, K. Nemoto, T. C. Ralph, J. P. Dowling, and G. J. Milburn, “Linear optical quantum computing with photonic qubits,” Rev. Mod. Phys. 79, 135–174 (2007).
[CrossRef]

J.-W. Pan, Z.-B. Chen, C.-Y. Lu, H. Weinfurter, A. Zeilinger, and M. Zukowski, “Multiphoton entanglement and interferometry,” Rev. Mod. Phys. 84, 777–838 (2012).
[CrossRef]

Science

M. Mariantoni, H. Wang, T. Yamamoto, M. Neeley, R. C. Bialczak, Y. Chen, M. Lenander, E. Lucero, A. D. OConnell, D. Sank, M. Weides, J. Wenner, Y. Yin, J. Zhao, A. N. Korotkov, A. N. Cleland, and J. M. Martinis, “Implementing the quantum von Neumann architecture with superconducting circuits,” Science 334, 61–65 (2011).
[CrossRef]

I. Fushman, D. Englund, A. Faraon, N. Stoltz, P. Petroff, and J. Vuckovic, “Controlled phase shifts with a single quantum dot,” Science 320, 769–772 (2008).
[CrossRef]

Other

C. W. Gardiner and P. Zoller, Quantum Noise (Springer, 2000).

M. K. Simon, Probability Distributions Involving Gaussian Random Variables, a Handbook for Engineers, Scientists and Mathematicians (Springer, 2006).

M. O. Scully and M. S. Zubairy, Quantum Optics (Cambridge University, 1997).

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

Schematic illustration of a two-photon polarization controlled arbitrary phase gate. Dotted red curves denote the first classical feed-forward (X feed-forward) based on the X^ measurement outcome, and the dashed green curve denotes the second classical feed-forward (Y feed-forward) according to the Y^ measurement outcome. The symbol conventions are as follows: “BSi(i=1,2), beam splitters; “PBSi(i=1,2,,6), polarization beam splitters; “Mi(i=1,2,,9), mirrors; “PS π,” “PS ±ξ,” and “PS ±ϕ,” the optical elements for realizing the required phase shifts π, ±ξ, and ±ϕ; “|αi(i=1,2), the probe coherent states; “±θ,” “θ,” the phase shifts of the probe coherent state; “|XX|,” X measurement; “|YY|,” Y measurement; “e, f, g” and “a, b, c, d,” the potential paths of photon 1 and photon 2; “Compi(i=1;2;3), the phase compensations for achieving the equal optical length of (path a and path b; path c and path d; the path photon 1 passing through and that of photon 2). Step I, Step II, and Step III are roughly marked off with blue dotted and dashed lines in this figure.

Fig. 2.
Fig. 2.

Schematic plot of the Gaussian probability distributions indicating the different X^ measurement outcomes. The dotted curves and the solid curves correspond to f(x,α1cosθ) and f(x,α1), respectively. The first group contains the left two curves plotting the probability distributions of the smaller β (α1scosθs and α1s), and the second group consists of the right two curves illustrating the probability distributions of the bigger ones (α1bcosθb and α1b).

Fig. 3.
Fig. 3.

Schematic illustration to depict the difference between the X^ measurement and the Y^ measurement on the probe coherent state. There are three color (red, blue, and green) curves, which indicate the probability distributions with the phase shifts (θ, 0, and θ) using the Y^ measurement, while the distributions of the phase shifts (θ and θ) cannot be distinguished by applying the X^ measurement.

Fig. 4.
Fig. 4.

Schematic plot of the error probability to distinguish two Gaussian distributions. The error probability decreases when enhancing the amplitude (α) of the probe coherent state and weakening the dissipated effect (γt) resulting from the external environment. Here, the dimensionless parameters are set as η2=1, θ=χt=1.05×104.

Tables (1)

Tables Icon

Table 1. Construction Process of Two-Photon Polarization Controlled Arbitrary Phase Gatea

Equations (31)

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

(α|HH+β|HV+γ|VH+δ|VV)12(α|HH+β|HV+γ|VH+eiξδ|VV)12,
Ucpm(|ϕs|αp)=eiHcpmt/[(a|0s+b|1s+c|2s+)|αp]=a|0s|αp+b|1s|αeiθp+c|2s|αe2iθp+,
12[(α|HHeb+β|HVeb+γ|VHfa+δ|VVfa)|α1+(α|HH+β|HV)ea|α1eiθ+(γ|VH+δ|VV)fb|α1eiθ],
12[(α|HH+β|HV)eb+(γ|VH+eiξδ|VV)fa],
12[eiϕ(x)(α|HH+eiξβ|HV)ea+eiϕ(x)(γ|VH+δ|VV)fb],
12[(α|HH+β|HV)ea+(γ|VH+eiξδ|VV)fb].
12[(α|HH+β|HV)eb+(γ|VH+eiξδ|VV)fa],Case2.1;12[(α|HH+β|HV)ea+(γ|VH+eiξδ|VV)fb],Case2.2.
12{|α2[(α|HH+β|HV)ed+(γ|VH+eiξδ|VV)fd]|α2eiθ[(α|HH+β|HV)ec(γ|VH+eiξδ|VV)fc]},
12[(α|HH+β|HV)ed+(γ|VH+eiξδ|VV)fd].
PBS212(α|HH+β|HV)+(γ|VH+eiξδ|VV)gd(12),
12[(α|HH+β|HV)ec(γ|VH+eiξδ|VV)fc],
12[(α|HH+β|HV)ec+(γ|VH+eiξδ|VV)fc],
12(α|HH+β|HV+γ|VH+eiξδ|VV)gd(12).
|ψx=x|ψ=12{x|α1eiθ(α|HH+β|HV)ea+x|α1eiθ(γ|VH+δ|VV)fb+x|α1[(γ|VH+δ|VV)fa+(α|HH+β|HV)eb]},
x|β=(2π)1/4exp[(Imβ)2(x2β)2/4],
|ψx=12{f(x,α1cosθ)[eiϕ(x)(α|HH+β|HV)ea+eiϕ(x)×(γ|VH+δ|VV)fb]+f(x,α1)[(γ|VH+δ|VV)fa+(α|HH+β|HV)eb]},
f(x,α1cosθ)=(2π)1/4exp[(x2α1cosθ)2/4],f(x,α1)=(2π)1/4exp[(x2α1)2/4].
Perr1=Q(xcx1)=12erfc[α1(1cosθ)/2].
|ψ=12{[(α|HH+β|HV)ed+(γ|VH+eiξδ|VV)fd]|α2[(α|HH+β|HV)ec(γ|VH+eiξδ|VV)fc]|α2eiθ},
|ψp=12[(α|HH+β|HV)ed+(γ|VH+eiξδ|VV)fd]×p|α212[(α|HH+β|HV)ec(γ|VH+eiξδ|VV)fc]p|α2eiθ,
p|β=(2π3)1/4exp[(Imβ)22iβpp2].
|ψp=12{f(p,0)e2ipα2[(α|HH+β|HV)ed+(γ|VH+eiξδ|VV)fd]f(p,α2sinθ)e2ipα2cosθ[(α|HH+β|HV)ec(γ|VH+eiξδ|VV)fc]},
f(p,α2sinθ)=(2π3)1/4exp[(pα2sinθ)2],f(p,0)=(2π3)1/4exp(p2),
Perr2=Q(pcp2)=12erfc[α2sinθ/22].
PerrPerr1+Perr2=12erfc[α1(1cosθ)/2]+12erfc[α2sinθ/22].
ρt=J^ρ+L^ρ,J^ρ=γaρa,L^ρ=γ2(aaρ+ρaa),
ρ(t)=D˜(t)ρ(0),
ρ(t)=[D˜(Δt)U˜(Δt)]Nρ(0).
|e,a=12(α|HH+β|HV)ea,|e,b=12(α|HH+β|HV)eb,|f,a=12(γ|VH+δ|VV)fa,|f,b=12(γ|VH+δ|VV)fb.
ρs(t)=|e,ae,a||A2αeiθA2αeiθ|+|e,be,b||A2αA2α|+C|e,be,a||A2αA2αeiθ|+C|e,af,a||A2αeiθA2α|+C*|e,ae,b||A2αeiθA2α|+CD|e,bf,b||A2αA2αeiθ|+CE|e,bf,a||A2αA2α|+CE|e,af,b||A2αeiθA2αeiθ|+C*|f,ae,a||A2αA2αeiθ|+C*D*|f,be,b||A2αeiθA2α|+C*E*|f,ae,b||A2αA2α|+C*E*|f,be,a||A2αeiθA2αeiθ|+|f,af,a||A2αA2α|+E*|f,bf,a||A2αeiθA2α|+E|f,af,b||A2αA2αeiθ|+|f,bf,b||A2αeiθA2αeiθ|,
A=eγ2t,C=exp{α2(1eγtN)×n=1Nexp[γ(n1)tN][1exp(iχntN)]},D=exp{(Aα)2(1eγt)(1exp(iχt)},E=exp{(Aα)2(1eγtN)×n=1Nexp[γ(n1)tN][1exp(iχntN)]}.

Metrics