Abstract

Multipartite entanglement is a resource for quantum communication and computation. Vector four-wave mixing (FWM) in a fiber, driven by two strong optical pumps, couples the evolution of four weak optical sidebands (modes). Depending on the fiber dispersion and pump frequencies, the mode frequencies can be similar (separated by less than 1 THz) or dissimilar (separated by more than 10 THz). In this report, the discrete- and continuous-variable entanglement produced by vector FWM is studied in detail. Formulas are derived for the variances of, and correlations between, the mode quadratures and photon numbers. These formulas and related results show that the modes are four-partite entangled.

© 2008 Optical Society of America

Full Article  |  PDF Article
Related Articles
Multipartite continuous-variable entanglement in nondegenerate optical parametric amplification system

Chao Ying Zhao, Wei Han Tan, Jiang Rong Xu, and Fan Ge
J. Opt. Soc. Am. B 28(5) 1067-1076 (2011)

Higher-capacity communication links based on two-mode phase-sensitive amplifiers

C. J. McKinstrie, N. Alic, Z. Tong, and M. Karlsson
Opt. Express 19(13) 11977-11991 (2011)

Creation of four-mode weighted cluster states with atomic ensembles in high-Q ring cavities

Li-hui Sun, Yan-qin Chen, and Gao-xiang Li
Opt. Express 20(3) 3176-3191 (2012)

References

  • View by:
  • |
  • |
  • |

  1. E. Schrödinger, “Die gegenwärtige Situation in der Quantenmechanik,” Naturwiss. 28, 807–812, 823–828 and 844–849 (1928).
  2. J. S. Bell, Speakable and Unspeakable in Quantum Mechanics, 2nd Ed. (Cambridge University Press, 2004).
    [Crossref]
  3. M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information (Cambridge University Press, 2000).
  4. S. L. Braunstein and A. K. Pati, Quantum Information with Continuous Variables (Kluwer Academic Press, 2003).
  5. C. H. Bennett and S. J. Wiesner, “Communication via one- and two-particle operators on Einstein-Podolsky-Rosen states,” Phys. Rev. Lett. 69, 2881–2884 (1992).
    [Crossref] [PubMed]
  6. K. Mattle, H. Weinfurter, P. G. Kwiat, and A. Zeilinger, “Dense coding in experimental quantum communications,” Phys. Rev. Lett. 76, 4656–4659 (1996).
    [Crossref] [PubMed]
  7. S. L. Braunstein and H. J. Kimble, “Dense coding for continuous variables,” Phys. Rev. A 61, 042302 (2000).
    [Crossref]
  8. X. Li, Q. Pan, J. Jing, J. Zhang, C. Xie, and K. Peng, “Quantum dense coding exploiting a bright Einstein-Podolsky-Rosen beam,” Phys. Rev. Lett. 88, 047904 (2002).
    [Crossref] [PubMed]
  9. J. Zhang, C. Xie, and K. Peng, “Controlled dense coding for continuous variables using three-partite entangled states,” Phys. Rev. A 66, 032318 (2002).
    [Crossref]
  10. J. Jing, J. Zhang, Y. Fan, F. Zhao, C. Xie, and K. Peng, “Experimental demonstration of tripartite entanglement and controlled dense coding for continuous variables,” Phys. Rev. Lett. 90, 167903 (2003).
    [Crossref] [PubMed]
  11. A. K. Ekert, “Quantum cryptography based on Bell’s theorem,” Phys. Rev. Lett. 67, 661–663 (1991).
    [Crossref] [PubMed]
  12. T. Jennewein, C. Simon, G. Weihs, H. Weinfurter, and A. Zeilinger, “Quantum cryptography with entangled photons,” Phys. Rev. Lett. 84, 4729–4732 (2000).
    [Crossref] [PubMed]
  13. D. S. Naik, C. G. Peterson, A. G. White, A. J. Berglund, and P. G. Kwiat, “Entangled state quantum cryptography: Eavesdropping on the Ekert protocol,” Phys. Rev. Lett. 84, 4733–4736 (2000).
    [Crossref] [PubMed]
  14. W. Tittel, J. Brendel, H. Zbinden, and N. Gisin, “Quantum cryptography using entangled photons in energy-time Bell states,” Phys. Rev. Lett. 84, 4737–4740 (2000).
    [Crossref] [PubMed]
  15. S. Gröblacher, T. Jennewein, A. Varizi, G. Weihs, and A. Zeilinger, “Experimental quantum cryptography with qutrits,” New J. Phys. 8, 75 (2006).
    [Crossref]
  16. R. Raussendorf and H. J. Briegel, “A one-way quantum computer,” Phys. Rev. Lett. 86, 5188–5191 (2001).
    [Crossref] [PubMed]
  17. M. A. Nielsen, “Optical quantum computing using cluster states,” Phys. Rev. Lett. 93, 040503 (2004).
    [Crossref] [PubMed]
  18. P. Walther, K. J. Resch, T. Rudolph, E. Schenk, H. Weinfurter, V. Vedral, M. Aspelmeyer, and A. Zeilinger, “Experimental one-way quantum computing,” Nature 434, 169–176 (2005).
    [Crossref] [PubMed]
  19. N. C. Menicucci, P. van Loock, M. Gu, C. Weedbrook, T. C. Ralph, and M. A. Nielsen, “Universal quantum computation with continuous-variable cluster states,” Phys. Rev. Lett. 97, 110501 (2006).
    [Crossref] [PubMed]
  20. C. H. Bennett, G. Brassard, C. Crepeau, R. Josza, A. Peres, and W. K. Wootters, “Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels,” Phys. Rev. Lett. 70, 1895–1899 (1993).
    [Crossref] [PubMed]
  21. D. Bouwmeester, J.W. Pan, K. Mattle, M. Eibl, H Weinfurter, and A. Zeilinger, “Experimental quantum teleportation,” Nature 390, 575–579 (1997).
    [Crossref]
  22. S. L. Braunstein and H. J. Kimble, “Teleportation of continuous quantum variables,” Phys. Rev. Lett. 80, 869–872 (1998).
    [Crossref]
  23. A. Furusawa, J. L. Sorensen, S. J. Braunstein, C. A. Fuchs, H. J. Kimble, and E. S. Polzik, “Unconditional quantum teleportation,” Science 282, 706–709 (1998).
    [Crossref] [PubMed]
  24. W. P. Bowen, N. Treps, B. C. Buchler, R. Schnabel, T. C. Ralph, H. A. Bachor, T. Symul, and P. K. Lam, “Experimental investigation of continuous-variable quantum teleportation,” Phys. Rev. A 67, 032302 (2003).
    [Crossref]
  25. T. C. Zhang, K. W. Goh, C. W. Chou, P. Lodahl, and H. J. Kimble, “Quantum teleportation of light beams,” Phys. Rev. A 67, 033802 (2003).
    [Crossref]
  26. P. van Loock and S. L. Braunstein, “Multipartite entanglement for continuous variables: A quantum teleportation network,” Phys. Rev. Lett. 84, 3482–3485 (2000).
    [Crossref] [PubMed]
  27. T. Aoki, N. Takei, H. Yonezawa, K. Wakui, T. Hiraoka, and A. Furusawa, “Experimental creation of a fully inseparable tripartite continuous-variable state,” Phys. Rev. Lett. 91, 080404 (2003).
    [Crossref] [PubMed]
  28. A. M. Lance, T. Symul, W. P. Bowen, B. C. Sanders, and P. K. Lam, “Tripartite quantum state sharing,” Phys. Rev. Lett. 92, 177903 (2004).
    [Crossref] [PubMed]
  29. H. Yonezawa, T. Aoki, and A. Furusawa, “Demonstration of a quantum teleportation network for continuous variabes,” Nature 431, 430–434 (2004).
    [Crossref] [PubMed]
  30. D. Bouwmeester, J. W. Pan, M. Daniell, H. Weinfurter, and A. Zeilinger, “Observation of three-photon Greenburger-Horne-Zeilinger entanglement,” Phys. Rev. Lett. 82, 1345–1349 (1999).
    [Crossref]
  31. J. W. Pan, M. Daniell, S. Gasparoni, G. Weihs, and A. Zeilinger, “Experimental demonstration of four-photon entanglement and high-fidelity teleportation,” Phys. Rev. Lett. 86, 4435–4438 (2001).
    [Crossref] [PubMed]
  32. N. Kiesel, C. Schmid, U. Weber, G. Toth, O. Guhne, R. Ursin, and H. Weinfurter, “Experimental analysis of a four-qubit photon cluster state,” Phys. Rev. Lett. 95, 210502 (2005).
    [Crossref] [PubMed]
  33. O. Glöckl, S. Lorenz, C. Marquardt, J. Heersink, M. Brownnutt, C. Silberhorn, Q. Pan, P. van Loock, N. Korolkova, and G. Leuchs, “Experiment towards continuous-variable entanglement swapping: Highly correlated four-partite quantum state,” Phys. Rev. A 68, 012319 (2003).
    [Crossref]
  34. X. Su, A. Tan, X. Jia, J. Zhang, C. Xie, and K. Peng, “Experimental preparation of quadripartite cluster and Greenberger-Horne-Zeilinger entangled states for continuous variables,” Phys. Rev. Lett. 98, 707502 (2007).
    [Crossref]
  35. D. C. Burnham and D. L. Weinberg, “Observation of simultaneity in parametric production of optical photon pairs,” Phys. Rev. Lett. 25, 84–87 (1970).
    [Crossref]
  36. P. G. Kwiat, K. Mattle, H Weinfurter, A. Zeilinger, A. V. Sergienko, and Y. Shih, “New high-intensity source of polarization-entangled photon pairs,” Phys. Rev. Lett. 75, 4337–4341 (1995).
    [Crossref] [PubMed]
  37. L. A. Wu, H. J. Kimble, J. L. Hall, and H. Wu, “Generation of squeezed states by parametric down conversion,” Phys. Rev. Lett. 57, 2520–2523 (1986).
    [Crossref] [PubMed]
  38. A. Ferraro, M. G. A. Paris, M. Bondani, A. Allevi, E. Puddu, and A. Andreoni, “Three-mode entanglement by interlinked nonlinear interactions in optical χ(2) media,” J. Opt. Soc. Am. B 21, 1241–1249 (2004).
    [Crossref]
  39. A. V. Rodionov and A. S. Chirkin, “Entangled photon states in consecutive nonlinear optical interactions,” JETP Lett. 79, 253–256 and 582 (2004).
    [Crossref]
  40. O. Pfister, S. Feng, G. Jennings, R. Pooser, and D. Xie, “Multipartite continuous-variable entanglement from concurrent nonlinearities,” Phys. Rev. A 70, 020302R (2004).
    [Crossref]
  41. R. C. Pooser and O. Pfister, “Observation of triply coincident nonlinearities in periodically poled KTiOPO4,” Opt. Lett. 30, 2635–2637 (2005).
    [Crossref] [PubMed]
  42. M. Bondani, A. Allevi, E. Gevinti, A. Agliati, and A. Andreoni, “3D phase-matching conditions for the generation of entangled triplets by χ(2) interlinked interactions,” Opt. Express 14, 9838–9843 (2006).
    [Crossref] [PubMed]
  43. M. Fiorentino, P. L. Voss, J. E. Sharping, and P. Kumar, “All-fiber photon-pair source for quantum communications,” IEEE Photon. Technol. Lett. 14, 983–985 (2002).
    [Crossref]
  44. J. E. Sharping, J. Chen, X. Li, and P. Kumar, “Quantum-correlated twin photons from microstructure fiber,” Opt. Express 12, 3086–3094 (2004).
    [Crossref] [PubMed]
  45. H. Takesue and K. Inoue, “Generation of polarization-entangled photon pairs and violation of Bell’s inequality using spontaneous four-wave mixing in a fiber loop,” Phys. Rev. A 70, 031802R (2004).
    [Crossref]
  46. J. G. Rarity, J. Fulconis, J. Duligall, W. J. Wadsworth, and P. S. J. Russell, “Photonic crystal fiber source of correlated photon pairs,” Opt. Express 13, 534–544 (2005).
    [Crossref] [PubMed]
  47. C. J. McKinstrie, J. D. Harvey, S. Radic, and M. G. Raymer, “Translation of quantum states by four-wave mixing in fibers,” Opt. Express 13, 9131–9142 (2005).
    [Crossref] [PubMed]
  48. C. J. McKinstrie, S. Radic, and A. R. Chraplyvy, “Parametric amplifiers driven by two pump waves,” IEEE J. Sel. Top. Quantum Electron. 8, 538–547 and 956 (2002).
    [Crossref]
  49. C. J. McKinstrie, S. Radic, and C. Xie, “Parametric instabilities driven by orthogonal pump waves in birefringent fibers,” Opt. Express 11, 2619–2633 (2003).
    [Crossref] [PubMed]
  50. C. J. McKinstrie, S. Radic, and M. G. Raymer, “Quantum noise properties of parametric amplifiers driven by two pump waves,” Opt. Express 12, 5037–5066 (2004).
    [Crossref] [PubMed]
  51. C. J. McKinstrie and M. G. Raymer, “Four-wave mixing cascades near the zero-dispersion frequency,” Opt. Express 14, 9600–9610 (2006).
    [Crossref] [PubMed]
  52. C. J. McKinstrie, S. Radic, M. G. Raymer, and L. Schenato, “Unimpaired phase-sensitive amplification by vector four-wave mixing near the zero-dispersion frequency,” Opt. Express 15, 2178–2189 (2007).
    [Crossref] [PubMed]
  53. C. J. McKinstrie and S. Radic, “Phase-sensitive amplification in a fiber,” Opt. Express 12, 4973–4979 (2004).
    [Crossref] [PubMed]
  54. J. Fan and A. Migdall, “Generation of cross-polarized photon pairs in a microstructure fiber with frequency-conjugate laser pump pulses,” Opt. Express 13, 5777–5782 (2005).
    [Crossref] [PubMed]
  55. S. Radic, C. J. McKinstrie, R. M. Jopson, J. C. Centanni, Q. Lin, and G. P. Agrawal, “Record performance of a parametric amplifier constructed with highly-nonlinear fiber,” Electron. Lett. 39, 838–839 (2003).
    [Crossref]
  56. Z. G. Lu, P. J. Bock, J. R. Liu, F. G. Sun, and T. J. Hall, “All-optical 1550 to 1310 nm wavelength converter,” Electron. Lett. 42, 937–938 (2006).
    [Crossref]
  57. W. H. Reeves, J. C. Knight, P. S. J. Russell, and P. J. Roberts, “Demonstration of ultra-flattened dispersion in photonic crystal fibers,” Opt. Express 10, 609–613 (2002).
    [PubMed]
  58. K. P. Hansen, “Dispersion flattened hybrid-core nonlinear photonic crystal fiber,” Opt. Express 11, 1503–1509 (2003).
    [Crossref] [PubMed]
  59. J.M Manley and H. E. Rowe, “Some general properties of nonlinear elements—Part I. General energy relations,” Proc. IRE 44, 904–913 (1956).
    [Crossref]
  60. M. T. Weiss, “Quantum derivation of energy relations analogous to those for nonlinear rectances,” Proc. IRE 45, 1012–1013 (1957).
  61. S. M. Barnett and P. M. Radmore, Methods in Theoretical Quantum Optics (Oxford University Press, 1997).
  62. R. Loudon, The Quantum Theory of Light, 3rd Ed. (Oxford University Press, 2000).
  63. C. J. McKinstrie, M. Yu, M. G. Raymer, and S. Radic, “Quantum noise properties of parametric processes in fibers,” Opt. Express 13, 4986–5012 (2005).
    [Crossref] [PubMed]
  64. S. J. van Enk, “Entanglement of electromagnetic fields,” Phys. Rev. A 67, 022303 (2003).
    [Crossref]
  65. K. N. Cassemiro, A. S. Villar, P. Valente, M. Martinelli, and P. Nussenzveig, “Experimental observation of three-color optical quantum correlations,” Opt. Lett. 32, 695–697 (2007).
    [Crossref] [PubMed]
  66. P. van Loock and A. Furusawa, “Detecting genuine multipartite continuous-variable entanglement,” Phys. Rev. A 67, 052315 (2003).
    [Crossref]

2007 (3)

2006 (5)

C. J. McKinstrie and M. G. Raymer, “Four-wave mixing cascades near the zero-dispersion frequency,” Opt. Express 14, 9600–9610 (2006).
[Crossref] [PubMed]

Z. G. Lu, P. J. Bock, J. R. Liu, F. G. Sun, and T. J. Hall, “All-optical 1550 to 1310 nm wavelength converter,” Electron. Lett. 42, 937–938 (2006).
[Crossref]

M. Bondani, A. Allevi, E. Gevinti, A. Agliati, and A. Andreoni, “3D phase-matching conditions for the generation of entangled triplets by χ(2) interlinked interactions,” Opt. Express 14, 9838–9843 (2006).
[Crossref] [PubMed]

S. Gröblacher, T. Jennewein, A. Varizi, G. Weihs, and A. Zeilinger, “Experimental quantum cryptography with qutrits,” New J. Phys. 8, 75 (2006).
[Crossref]

N. C. Menicucci, P. van Loock, M. Gu, C. Weedbrook, T. C. Ralph, and M. A. Nielsen, “Universal quantum computation with continuous-variable cluster states,” Phys. Rev. Lett. 97, 110501 (2006).
[Crossref] [PubMed]

2005 (7)

2004 (10)

C. J. McKinstrie and S. Radic, “Phase-sensitive amplification in a fiber,” Opt. Express 12, 4973–4979 (2004).
[Crossref] [PubMed]

C. J. McKinstrie, S. Radic, and M. G. Raymer, “Quantum noise properties of parametric amplifiers driven by two pump waves,” Opt. Express 12, 5037–5066 (2004).
[Crossref] [PubMed]

J. E. Sharping, J. Chen, X. Li, and P. Kumar, “Quantum-correlated twin photons from microstructure fiber,” Opt. Express 12, 3086–3094 (2004).
[Crossref] [PubMed]

H. Takesue and K. Inoue, “Generation of polarization-entangled photon pairs and violation of Bell’s inequality using spontaneous four-wave mixing in a fiber loop,” Phys. Rev. A 70, 031802R (2004).
[Crossref]

A. Ferraro, M. G. A. Paris, M. Bondani, A. Allevi, E. Puddu, and A. Andreoni, “Three-mode entanglement by interlinked nonlinear interactions in optical χ(2) media,” J. Opt. Soc. Am. B 21, 1241–1249 (2004).
[Crossref]

A. V. Rodionov and A. S. Chirkin, “Entangled photon states in consecutive nonlinear optical interactions,” JETP Lett. 79, 253–256 and 582 (2004).
[Crossref]

O. Pfister, S. Feng, G. Jennings, R. Pooser, and D. Xie, “Multipartite continuous-variable entanglement from concurrent nonlinearities,” Phys. Rev. A 70, 020302R (2004).
[Crossref]

A. M. Lance, T. Symul, W. P. Bowen, B. C. Sanders, and P. K. Lam, “Tripartite quantum state sharing,” Phys. Rev. Lett. 92, 177903 (2004).
[Crossref] [PubMed]

H. Yonezawa, T. Aoki, and A. Furusawa, “Demonstration of a quantum teleportation network for continuous variabes,” Nature 431, 430–434 (2004).
[Crossref] [PubMed]

M. A. Nielsen, “Optical quantum computing using cluster states,” Phys. Rev. Lett. 93, 040503 (2004).
[Crossref] [PubMed]

2003 (10)

J. Jing, J. Zhang, Y. Fan, F. Zhao, C. Xie, and K. Peng, “Experimental demonstration of tripartite entanglement and controlled dense coding for continuous variables,” Phys. Rev. Lett. 90, 167903 (2003).
[Crossref] [PubMed]

T. Aoki, N. Takei, H. Yonezawa, K. Wakui, T. Hiraoka, and A. Furusawa, “Experimental creation of a fully inseparable tripartite continuous-variable state,” Phys. Rev. Lett. 91, 080404 (2003).
[Crossref] [PubMed]

W. P. Bowen, N. Treps, B. C. Buchler, R. Schnabel, T. C. Ralph, H. A. Bachor, T. Symul, and P. K. Lam, “Experimental investigation of continuous-variable quantum teleportation,” Phys. Rev. A 67, 032302 (2003).
[Crossref]

T. C. Zhang, K. W. Goh, C. W. Chou, P. Lodahl, and H. J. Kimble, “Quantum teleportation of light beams,” Phys. Rev. A 67, 033802 (2003).
[Crossref]

O. Glöckl, S. Lorenz, C. Marquardt, J. Heersink, M. Brownnutt, C. Silberhorn, Q. Pan, P. van Loock, N. Korolkova, and G. Leuchs, “Experiment towards continuous-variable entanglement swapping: Highly correlated four-partite quantum state,” Phys. Rev. A 68, 012319 (2003).
[Crossref]

C. J. McKinstrie, S. Radic, and C. Xie, “Parametric instabilities driven by orthogonal pump waves in birefringent fibers,” Opt. Express 11, 2619–2633 (2003).
[Crossref] [PubMed]

S. Radic, C. J. McKinstrie, R. M. Jopson, J. C. Centanni, Q. Lin, and G. P. Agrawal, “Record performance of a parametric amplifier constructed with highly-nonlinear fiber,” Electron. Lett. 39, 838–839 (2003).
[Crossref]

S. J. van Enk, “Entanglement of electromagnetic fields,” Phys. Rev. A 67, 022303 (2003).
[Crossref]

P. van Loock and A. Furusawa, “Detecting genuine multipartite continuous-variable entanglement,” Phys. Rev. A 67, 052315 (2003).
[Crossref]

K. P. Hansen, “Dispersion flattened hybrid-core nonlinear photonic crystal fiber,” Opt. Express 11, 1503–1509 (2003).
[Crossref] [PubMed]

2002 (5)

W. H. Reeves, J. C. Knight, P. S. J. Russell, and P. J. Roberts, “Demonstration of ultra-flattened dispersion in photonic crystal fibers,” Opt. Express 10, 609–613 (2002).
[PubMed]

C. J. McKinstrie, S. Radic, and A. R. Chraplyvy, “Parametric amplifiers driven by two pump waves,” IEEE J. Sel. Top. Quantum Electron. 8, 538–547 and 956 (2002).
[Crossref]

M. Fiorentino, P. L. Voss, J. E. Sharping, and P. Kumar, “All-fiber photon-pair source for quantum communications,” IEEE Photon. Technol. Lett. 14, 983–985 (2002).
[Crossref]

X. Li, Q. Pan, J. Jing, J. Zhang, C. Xie, and K. Peng, “Quantum dense coding exploiting a bright Einstein-Podolsky-Rosen beam,” Phys. Rev. Lett. 88, 047904 (2002).
[Crossref] [PubMed]

J. Zhang, C. Xie, and K. Peng, “Controlled dense coding for continuous variables using three-partite entangled states,” Phys. Rev. A 66, 032318 (2002).
[Crossref]

2001 (2)

R. Raussendorf and H. J. Briegel, “A one-way quantum computer,” Phys. Rev. Lett. 86, 5188–5191 (2001).
[Crossref] [PubMed]

J. W. Pan, M. Daniell, S. Gasparoni, G. Weihs, and A. Zeilinger, “Experimental demonstration of four-photon entanglement and high-fidelity teleportation,” Phys. Rev. Lett. 86, 4435–4438 (2001).
[Crossref] [PubMed]

2000 (5)

T. Jennewein, C. Simon, G. Weihs, H. Weinfurter, and A. Zeilinger, “Quantum cryptography with entangled photons,” Phys. Rev. Lett. 84, 4729–4732 (2000).
[Crossref] [PubMed]

D. S. Naik, C. G. Peterson, A. G. White, A. J. Berglund, and P. G. Kwiat, “Entangled state quantum cryptography: Eavesdropping on the Ekert protocol,” Phys. Rev. Lett. 84, 4733–4736 (2000).
[Crossref] [PubMed]

W. Tittel, J. Brendel, H. Zbinden, and N. Gisin, “Quantum cryptography using entangled photons in energy-time Bell states,” Phys. Rev. Lett. 84, 4737–4740 (2000).
[Crossref] [PubMed]

S. L. Braunstein and H. J. Kimble, “Dense coding for continuous variables,” Phys. Rev. A 61, 042302 (2000).
[Crossref]

P. van Loock and S. L. Braunstein, “Multipartite entanglement for continuous variables: A quantum teleportation network,” Phys. Rev. Lett. 84, 3482–3485 (2000).
[Crossref] [PubMed]

1999 (1)

D. Bouwmeester, J. W. Pan, M. Daniell, H. Weinfurter, and A. Zeilinger, “Observation of three-photon Greenburger-Horne-Zeilinger entanglement,” Phys. Rev. Lett. 82, 1345–1349 (1999).
[Crossref]

1998 (2)

S. L. Braunstein and H. J. Kimble, “Teleportation of continuous quantum variables,” Phys. Rev. Lett. 80, 869–872 (1998).
[Crossref]

A. Furusawa, J. L. Sorensen, S. J. Braunstein, C. A. Fuchs, H. J. Kimble, and E. S. Polzik, “Unconditional quantum teleportation,” Science 282, 706–709 (1998).
[Crossref] [PubMed]

1997 (1)

D. Bouwmeester, J.W. Pan, K. Mattle, M. Eibl, H Weinfurter, and A. Zeilinger, “Experimental quantum teleportation,” Nature 390, 575–579 (1997).
[Crossref]

1996 (1)

K. Mattle, H. Weinfurter, P. G. Kwiat, and A. Zeilinger, “Dense coding in experimental quantum communications,” Phys. Rev. Lett. 76, 4656–4659 (1996).
[Crossref] [PubMed]

1995 (1)

P. G. Kwiat, K. Mattle, H Weinfurter, A. Zeilinger, A. V. Sergienko, and Y. Shih, “New high-intensity source of polarization-entangled photon pairs,” Phys. Rev. Lett. 75, 4337–4341 (1995).
[Crossref] [PubMed]

1993 (1)

C. H. Bennett, G. Brassard, C. Crepeau, R. Josza, A. Peres, and W. K. Wootters, “Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels,” Phys. Rev. Lett. 70, 1895–1899 (1993).
[Crossref] [PubMed]

1992 (1)

C. H. Bennett and S. J. Wiesner, “Communication via one- and two-particle operators on Einstein-Podolsky-Rosen states,” Phys. Rev. Lett. 69, 2881–2884 (1992).
[Crossref] [PubMed]

1991 (1)

A. K. Ekert, “Quantum cryptography based on Bell’s theorem,” Phys. Rev. Lett. 67, 661–663 (1991).
[Crossref] [PubMed]

1986 (1)

L. A. Wu, H. J. Kimble, J. L. Hall, and H. Wu, “Generation of squeezed states by parametric down conversion,” Phys. Rev. Lett. 57, 2520–2523 (1986).
[Crossref] [PubMed]

1970 (1)

D. C. Burnham and D. L. Weinberg, “Observation of simultaneity in parametric production of optical photon pairs,” Phys. Rev. Lett. 25, 84–87 (1970).
[Crossref]

1957 (1)

M. T. Weiss, “Quantum derivation of energy relations analogous to those for nonlinear rectances,” Proc. IRE 45, 1012–1013 (1957).

1956 (1)

J.M Manley and H. E. Rowe, “Some general properties of nonlinear elements—Part I. General energy relations,” Proc. IRE 44, 904–913 (1956).
[Crossref]

1928 (1)

E. Schrödinger, “Die gegenwärtige Situation in der Quantenmechanik,” Naturwiss. 28, 807–812, 823–828 and 844–849 (1928).

Agliati, A.

Agrawal, G. P.

S. Radic, C. J. McKinstrie, R. M. Jopson, J. C. Centanni, Q. Lin, and G. P. Agrawal, “Record performance of a parametric amplifier constructed with highly-nonlinear fiber,” Electron. Lett. 39, 838–839 (2003).
[Crossref]

Allevi, A.

Andreoni, A.

Aoki, T.

H. Yonezawa, T. Aoki, and A. Furusawa, “Demonstration of a quantum teleportation network for continuous variabes,” Nature 431, 430–434 (2004).
[Crossref] [PubMed]

T. Aoki, N. Takei, H. Yonezawa, K. Wakui, T. Hiraoka, and A. Furusawa, “Experimental creation of a fully inseparable tripartite continuous-variable state,” Phys. Rev. Lett. 91, 080404 (2003).
[Crossref] [PubMed]

Aspelmeyer, M.

P. Walther, K. J. Resch, T. Rudolph, E. Schenk, H. Weinfurter, V. Vedral, M. Aspelmeyer, and A. Zeilinger, “Experimental one-way quantum computing,” Nature 434, 169–176 (2005).
[Crossref] [PubMed]

Bachor, H. A.

W. P. Bowen, N. Treps, B. C. Buchler, R. Schnabel, T. C. Ralph, H. A. Bachor, T. Symul, and P. K. Lam, “Experimental investigation of continuous-variable quantum teleportation,” Phys. Rev. A 67, 032302 (2003).
[Crossref]

Barnett, S. M.

S. M. Barnett and P. M. Radmore, Methods in Theoretical Quantum Optics (Oxford University Press, 1997).

Bell, J. S.

J. S. Bell, Speakable and Unspeakable in Quantum Mechanics, 2nd Ed. (Cambridge University Press, 2004).
[Crossref]

Bennett, C. H.

C. H. Bennett, G. Brassard, C. Crepeau, R. Josza, A. Peres, and W. K. Wootters, “Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels,” Phys. Rev. Lett. 70, 1895–1899 (1993).
[Crossref] [PubMed]

C. H. Bennett and S. J. Wiesner, “Communication via one- and two-particle operators on Einstein-Podolsky-Rosen states,” Phys. Rev. Lett. 69, 2881–2884 (1992).
[Crossref] [PubMed]

Berglund, A. J.

D. S. Naik, C. G. Peterson, A. G. White, A. J. Berglund, and P. G. Kwiat, “Entangled state quantum cryptography: Eavesdropping on the Ekert protocol,” Phys. Rev. Lett. 84, 4733–4736 (2000).
[Crossref] [PubMed]

Bock, P. J.

Z. G. Lu, P. J. Bock, J. R. Liu, F. G. Sun, and T. J. Hall, “All-optical 1550 to 1310 nm wavelength converter,” Electron. Lett. 42, 937–938 (2006).
[Crossref]

Bondani, M.

Bouwmeester, D.

D. Bouwmeester, J. W. Pan, M. Daniell, H. Weinfurter, and A. Zeilinger, “Observation of three-photon Greenburger-Horne-Zeilinger entanglement,” Phys. Rev. Lett. 82, 1345–1349 (1999).
[Crossref]

D. Bouwmeester, J.W. Pan, K. Mattle, M. Eibl, H Weinfurter, and A. Zeilinger, “Experimental quantum teleportation,” Nature 390, 575–579 (1997).
[Crossref]

Bowen, W. P.

A. M. Lance, T. Symul, W. P. Bowen, B. C. Sanders, and P. K. Lam, “Tripartite quantum state sharing,” Phys. Rev. Lett. 92, 177903 (2004).
[Crossref] [PubMed]

W. P. Bowen, N. Treps, B. C. Buchler, R. Schnabel, T. C. Ralph, H. A. Bachor, T. Symul, and P. K. Lam, “Experimental investigation of continuous-variable quantum teleportation,” Phys. Rev. A 67, 032302 (2003).
[Crossref]

Brassard, G.

C. H. Bennett, G. Brassard, C. Crepeau, R. Josza, A. Peres, and W. K. Wootters, “Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels,” Phys. Rev. Lett. 70, 1895–1899 (1993).
[Crossref] [PubMed]

Braunstein, S. J.

A. Furusawa, J. L. Sorensen, S. J. Braunstein, C. A. Fuchs, H. J. Kimble, and E. S. Polzik, “Unconditional quantum teleportation,” Science 282, 706–709 (1998).
[Crossref] [PubMed]

Braunstein, S. L.

P. van Loock and S. L. Braunstein, “Multipartite entanglement for continuous variables: A quantum teleportation network,” Phys. Rev. Lett. 84, 3482–3485 (2000).
[Crossref] [PubMed]

S. L. Braunstein and H. J. Kimble, “Dense coding for continuous variables,” Phys. Rev. A 61, 042302 (2000).
[Crossref]

S. L. Braunstein and H. J. Kimble, “Teleportation of continuous quantum variables,” Phys. Rev. Lett. 80, 869–872 (1998).
[Crossref]

S. L. Braunstein and A. K. Pati, Quantum Information with Continuous Variables (Kluwer Academic Press, 2003).

Brendel, J.

W. Tittel, J. Brendel, H. Zbinden, and N. Gisin, “Quantum cryptography using entangled photons in energy-time Bell states,” Phys. Rev. Lett. 84, 4737–4740 (2000).
[Crossref] [PubMed]

Briegel, H. J.

R. Raussendorf and H. J. Briegel, “A one-way quantum computer,” Phys. Rev. Lett. 86, 5188–5191 (2001).
[Crossref] [PubMed]

Brownnutt, M.

O. Glöckl, S. Lorenz, C. Marquardt, J. Heersink, M. Brownnutt, C. Silberhorn, Q. Pan, P. van Loock, N. Korolkova, and G. Leuchs, “Experiment towards continuous-variable entanglement swapping: Highly correlated four-partite quantum state,” Phys. Rev. A 68, 012319 (2003).
[Crossref]

Buchler, B. C.

W. P. Bowen, N. Treps, B. C. Buchler, R. Schnabel, T. C. Ralph, H. A. Bachor, T. Symul, and P. K. Lam, “Experimental investigation of continuous-variable quantum teleportation,” Phys. Rev. A 67, 032302 (2003).
[Crossref]

Burnham, D. C.

D. C. Burnham and D. L. Weinberg, “Observation of simultaneity in parametric production of optical photon pairs,” Phys. Rev. Lett. 25, 84–87 (1970).
[Crossref]

Cassemiro, K. N.

Centanni, J. C.

S. Radic, C. J. McKinstrie, R. M. Jopson, J. C. Centanni, Q. Lin, and G. P. Agrawal, “Record performance of a parametric amplifier constructed with highly-nonlinear fiber,” Electron. Lett. 39, 838–839 (2003).
[Crossref]

Chen, J.

Chirkin, A. S.

A. V. Rodionov and A. S. Chirkin, “Entangled photon states in consecutive nonlinear optical interactions,” JETP Lett. 79, 253–256 and 582 (2004).
[Crossref]

Chou, C. W.

T. C. Zhang, K. W. Goh, C. W. Chou, P. Lodahl, and H. J. Kimble, “Quantum teleportation of light beams,” Phys. Rev. A 67, 033802 (2003).
[Crossref]

Chraplyvy, A. R.

C. J. McKinstrie, S. Radic, and A. R. Chraplyvy, “Parametric amplifiers driven by two pump waves,” IEEE J. Sel. Top. Quantum Electron. 8, 538–547 and 956 (2002).
[Crossref]

Chuang, I. L.

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

Crepeau, C.

C. H. Bennett, G. Brassard, C. Crepeau, R. Josza, A. Peres, and W. K. Wootters, “Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels,” Phys. Rev. Lett. 70, 1895–1899 (1993).
[Crossref] [PubMed]

Daniell, M.

J. W. Pan, M. Daniell, S. Gasparoni, G. Weihs, and A. Zeilinger, “Experimental demonstration of four-photon entanglement and high-fidelity teleportation,” Phys. Rev. Lett. 86, 4435–4438 (2001).
[Crossref] [PubMed]

D. Bouwmeester, J. W. Pan, M. Daniell, H. Weinfurter, and A. Zeilinger, “Observation of three-photon Greenburger-Horne-Zeilinger entanglement,” Phys. Rev. Lett. 82, 1345–1349 (1999).
[Crossref]

Duligall, J.

Eibl, M.

D. Bouwmeester, J.W. Pan, K. Mattle, M. Eibl, H Weinfurter, and A. Zeilinger, “Experimental quantum teleportation,” Nature 390, 575–579 (1997).
[Crossref]

Ekert, A. K.

A. K. Ekert, “Quantum cryptography based on Bell’s theorem,” Phys. Rev. Lett. 67, 661–663 (1991).
[Crossref] [PubMed]

Fan, J.

Fan, Y.

J. Jing, J. Zhang, Y. Fan, F. Zhao, C. Xie, and K. Peng, “Experimental demonstration of tripartite entanglement and controlled dense coding for continuous variables,” Phys. Rev. Lett. 90, 167903 (2003).
[Crossref] [PubMed]

Feng, S.

O. Pfister, S. Feng, G. Jennings, R. Pooser, and D. Xie, “Multipartite continuous-variable entanglement from concurrent nonlinearities,” Phys. Rev. A 70, 020302R (2004).
[Crossref]

Ferraro, A.

Fiorentino, M.

M. Fiorentino, P. L. Voss, J. E. Sharping, and P. Kumar, “All-fiber photon-pair source for quantum communications,” IEEE Photon. Technol. Lett. 14, 983–985 (2002).
[Crossref]

Fuchs, C. A.

A. Furusawa, J. L. Sorensen, S. J. Braunstein, C. A. Fuchs, H. J. Kimble, and E. S. Polzik, “Unconditional quantum teleportation,” Science 282, 706–709 (1998).
[Crossref] [PubMed]

Fulconis, J.

Furusawa, A.

H. Yonezawa, T. Aoki, and A. Furusawa, “Demonstration of a quantum teleportation network for continuous variabes,” Nature 431, 430–434 (2004).
[Crossref] [PubMed]

T. Aoki, N. Takei, H. Yonezawa, K. Wakui, T. Hiraoka, and A. Furusawa, “Experimental creation of a fully inseparable tripartite continuous-variable state,” Phys. Rev. Lett. 91, 080404 (2003).
[Crossref] [PubMed]

P. van Loock and A. Furusawa, “Detecting genuine multipartite continuous-variable entanglement,” Phys. Rev. A 67, 052315 (2003).
[Crossref]

A. Furusawa, J. L. Sorensen, S. J. Braunstein, C. A. Fuchs, H. J. Kimble, and E. S. Polzik, “Unconditional quantum teleportation,” Science 282, 706–709 (1998).
[Crossref] [PubMed]

Gasparoni, S.

J. W. Pan, M. Daniell, S. Gasparoni, G. Weihs, and A. Zeilinger, “Experimental demonstration of four-photon entanglement and high-fidelity teleportation,” Phys. Rev. Lett. 86, 4435–4438 (2001).
[Crossref] [PubMed]

Gevinti, E.

Gisin, N.

W. Tittel, J. Brendel, H. Zbinden, and N. Gisin, “Quantum cryptography using entangled photons in energy-time Bell states,” Phys. Rev. Lett. 84, 4737–4740 (2000).
[Crossref] [PubMed]

Glöckl, O.

O. Glöckl, S. Lorenz, C. Marquardt, J. Heersink, M. Brownnutt, C. Silberhorn, Q. Pan, P. van Loock, N. Korolkova, and G. Leuchs, “Experiment towards continuous-variable entanglement swapping: Highly correlated four-partite quantum state,” Phys. Rev. A 68, 012319 (2003).
[Crossref]

Goh, K. W.

T. C. Zhang, K. W. Goh, C. W. Chou, P. Lodahl, and H. J. Kimble, “Quantum teleportation of light beams,” Phys. Rev. A 67, 033802 (2003).
[Crossref]

Gröblacher, S.

S. Gröblacher, T. Jennewein, A. Varizi, G. Weihs, and A. Zeilinger, “Experimental quantum cryptography with qutrits,” New J. Phys. 8, 75 (2006).
[Crossref]

Gu, M.

N. C. Menicucci, P. van Loock, M. Gu, C. Weedbrook, T. C. Ralph, and M. A. Nielsen, “Universal quantum computation with continuous-variable cluster states,” Phys. Rev. Lett. 97, 110501 (2006).
[Crossref] [PubMed]

Guhne, O.

N. Kiesel, C. Schmid, U. Weber, G. Toth, O. Guhne, R. Ursin, and H. Weinfurter, “Experimental analysis of a four-qubit photon cluster state,” Phys. Rev. Lett. 95, 210502 (2005).
[Crossref] [PubMed]

Hall, J. L.

L. A. Wu, H. J. Kimble, J. L. Hall, and H. Wu, “Generation of squeezed states by parametric down conversion,” Phys. Rev. Lett. 57, 2520–2523 (1986).
[Crossref] [PubMed]

Hall, T. J.

Z. G. Lu, P. J. Bock, J. R. Liu, F. G. Sun, and T. J. Hall, “All-optical 1550 to 1310 nm wavelength converter,” Electron. Lett. 42, 937–938 (2006).
[Crossref]

Hansen, K. P.

Harvey, J. D.

Heersink, J.

O. Glöckl, S. Lorenz, C. Marquardt, J. Heersink, M. Brownnutt, C. Silberhorn, Q. Pan, P. van Loock, N. Korolkova, and G. Leuchs, “Experiment towards continuous-variable entanglement swapping: Highly correlated four-partite quantum state,” Phys. Rev. A 68, 012319 (2003).
[Crossref]

Hiraoka, T.

T. Aoki, N. Takei, H. Yonezawa, K. Wakui, T. Hiraoka, and A. Furusawa, “Experimental creation of a fully inseparable tripartite continuous-variable state,” Phys. Rev. Lett. 91, 080404 (2003).
[Crossref] [PubMed]

Inoue, K.

H. Takesue and K. Inoue, “Generation of polarization-entangled photon pairs and violation of Bell’s inequality using spontaneous four-wave mixing in a fiber loop,” Phys. Rev. A 70, 031802R (2004).
[Crossref]

Jennewein, T.

S. Gröblacher, T. Jennewein, A. Varizi, G. Weihs, and A. Zeilinger, “Experimental quantum cryptography with qutrits,” New J. Phys. 8, 75 (2006).
[Crossref]

T. Jennewein, C. Simon, G. Weihs, H. Weinfurter, and A. Zeilinger, “Quantum cryptography with entangled photons,” Phys. Rev. Lett. 84, 4729–4732 (2000).
[Crossref] [PubMed]

Jennings, G.

O. Pfister, S. Feng, G. Jennings, R. Pooser, and D. Xie, “Multipartite continuous-variable entanglement from concurrent nonlinearities,” Phys. Rev. A 70, 020302R (2004).
[Crossref]

Jia, X.

X. Su, A. Tan, X. Jia, J. Zhang, C. Xie, and K. Peng, “Experimental preparation of quadripartite cluster and Greenberger-Horne-Zeilinger entangled states for continuous variables,” Phys. Rev. Lett. 98, 707502 (2007).
[Crossref]

Jing, J.

J. Jing, J. Zhang, Y. Fan, F. Zhao, C. Xie, and K. Peng, “Experimental demonstration of tripartite entanglement and controlled dense coding for continuous variables,” Phys. Rev. Lett. 90, 167903 (2003).
[Crossref] [PubMed]

X. Li, Q. Pan, J. Jing, J. Zhang, C. Xie, and K. Peng, “Quantum dense coding exploiting a bright Einstein-Podolsky-Rosen beam,” Phys. Rev. Lett. 88, 047904 (2002).
[Crossref] [PubMed]

Jopson, R. M.

S. Radic, C. J. McKinstrie, R. M. Jopson, J. C. Centanni, Q. Lin, and G. P. Agrawal, “Record performance of a parametric amplifier constructed with highly-nonlinear fiber,” Electron. Lett. 39, 838–839 (2003).
[Crossref]

Josza, R.

C. H. Bennett, G. Brassard, C. Crepeau, R. Josza, A. Peres, and W. K. Wootters, “Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels,” Phys. Rev. Lett. 70, 1895–1899 (1993).
[Crossref] [PubMed]

Kiesel, N.

N. Kiesel, C. Schmid, U. Weber, G. Toth, O. Guhne, R. Ursin, and H. Weinfurter, “Experimental analysis of a four-qubit photon cluster state,” Phys. Rev. Lett. 95, 210502 (2005).
[Crossref] [PubMed]

Kimble, H. J.

T. C. Zhang, K. W. Goh, C. W. Chou, P. Lodahl, and H. J. Kimble, “Quantum teleportation of light beams,” Phys. Rev. A 67, 033802 (2003).
[Crossref]

S. L. Braunstein and H. J. Kimble, “Dense coding for continuous variables,” Phys. Rev. A 61, 042302 (2000).
[Crossref]

S. L. Braunstein and H. J. Kimble, “Teleportation of continuous quantum variables,” Phys. Rev. Lett. 80, 869–872 (1998).
[Crossref]

A. Furusawa, J. L. Sorensen, S. J. Braunstein, C. A. Fuchs, H. J. Kimble, and E. S. Polzik, “Unconditional quantum teleportation,” Science 282, 706–709 (1998).
[Crossref] [PubMed]

L. A. Wu, H. J. Kimble, J. L. Hall, and H. Wu, “Generation of squeezed states by parametric down conversion,” Phys. Rev. Lett. 57, 2520–2523 (1986).
[Crossref] [PubMed]

Knight, J. C.

Korolkova, N.

O. Glöckl, S. Lorenz, C. Marquardt, J. Heersink, M. Brownnutt, C. Silberhorn, Q. Pan, P. van Loock, N. Korolkova, and G. Leuchs, “Experiment towards continuous-variable entanglement swapping: Highly correlated four-partite quantum state,” Phys. Rev. A 68, 012319 (2003).
[Crossref]

Kumar, P.

J. E. Sharping, J. Chen, X. Li, and P. Kumar, “Quantum-correlated twin photons from microstructure fiber,” Opt. Express 12, 3086–3094 (2004).
[Crossref] [PubMed]

M. Fiorentino, P. L. Voss, J. E. Sharping, and P. Kumar, “All-fiber photon-pair source for quantum communications,” IEEE Photon. Technol. Lett. 14, 983–985 (2002).
[Crossref]

Kwiat, P. G.

D. S. Naik, C. G. Peterson, A. G. White, A. J. Berglund, and P. G. Kwiat, “Entangled state quantum cryptography: Eavesdropping on the Ekert protocol,” Phys. Rev. Lett. 84, 4733–4736 (2000).
[Crossref] [PubMed]

K. Mattle, H. Weinfurter, P. G. Kwiat, and A. Zeilinger, “Dense coding in experimental quantum communications,” Phys. Rev. Lett. 76, 4656–4659 (1996).
[Crossref] [PubMed]

P. G. Kwiat, K. Mattle, H Weinfurter, A. Zeilinger, A. V. Sergienko, and Y. Shih, “New high-intensity source of polarization-entangled photon pairs,” Phys. Rev. Lett. 75, 4337–4341 (1995).
[Crossref] [PubMed]

Lam, P. K.

A. M. Lance, T. Symul, W. P. Bowen, B. C. Sanders, and P. K. Lam, “Tripartite quantum state sharing,” Phys. Rev. Lett. 92, 177903 (2004).
[Crossref] [PubMed]

W. P. Bowen, N. Treps, B. C. Buchler, R. Schnabel, T. C. Ralph, H. A. Bachor, T. Symul, and P. K. Lam, “Experimental investigation of continuous-variable quantum teleportation,” Phys. Rev. A 67, 032302 (2003).
[Crossref]

Lance, A. M.

A. M. Lance, T. Symul, W. P. Bowen, B. C. Sanders, and P. K. Lam, “Tripartite quantum state sharing,” Phys. Rev. Lett. 92, 177903 (2004).
[Crossref] [PubMed]

Leuchs, G.

O. Glöckl, S. Lorenz, C. Marquardt, J. Heersink, M. Brownnutt, C. Silberhorn, Q. Pan, P. van Loock, N. Korolkova, and G. Leuchs, “Experiment towards continuous-variable entanglement swapping: Highly correlated four-partite quantum state,” Phys. Rev. A 68, 012319 (2003).
[Crossref]

Li, X.

J. E. Sharping, J. Chen, X. Li, and P. Kumar, “Quantum-correlated twin photons from microstructure fiber,” Opt. Express 12, 3086–3094 (2004).
[Crossref] [PubMed]

X. Li, Q. Pan, J. Jing, J. Zhang, C. Xie, and K. Peng, “Quantum dense coding exploiting a bright Einstein-Podolsky-Rosen beam,” Phys. Rev. Lett. 88, 047904 (2002).
[Crossref] [PubMed]

Lin, Q.

S. Radic, C. J. McKinstrie, R. M. Jopson, J. C. Centanni, Q. Lin, and G. P. Agrawal, “Record performance of a parametric amplifier constructed with highly-nonlinear fiber,” Electron. Lett. 39, 838–839 (2003).
[Crossref]

Liu, J. R.

Z. G. Lu, P. J. Bock, J. R. Liu, F. G. Sun, and T. J. Hall, “All-optical 1550 to 1310 nm wavelength converter,” Electron. Lett. 42, 937–938 (2006).
[Crossref]

Lodahl, P.

T. C. Zhang, K. W. Goh, C. W. Chou, P. Lodahl, and H. J. Kimble, “Quantum teleportation of light beams,” Phys. Rev. A 67, 033802 (2003).
[Crossref]

Lorenz, S.

O. Glöckl, S. Lorenz, C. Marquardt, J. Heersink, M. Brownnutt, C. Silberhorn, Q. Pan, P. van Loock, N. Korolkova, and G. Leuchs, “Experiment towards continuous-variable entanglement swapping: Highly correlated four-partite quantum state,” Phys. Rev. A 68, 012319 (2003).
[Crossref]

Loudon, R.

R. Loudon, The Quantum Theory of Light, 3rd Ed. (Oxford University Press, 2000).

Lu, Z. G.

Z. G. Lu, P. J. Bock, J. R. Liu, F. G. Sun, and T. J. Hall, “All-optical 1550 to 1310 nm wavelength converter,” Electron. Lett. 42, 937–938 (2006).
[Crossref]

Manley, J.M

J.M Manley and H. E. Rowe, “Some general properties of nonlinear elements—Part I. General energy relations,” Proc. IRE 44, 904–913 (1956).
[Crossref]

Marquardt, C.

O. Glöckl, S. Lorenz, C. Marquardt, J. Heersink, M. Brownnutt, C. Silberhorn, Q. Pan, P. van Loock, N. Korolkova, and G. Leuchs, “Experiment towards continuous-variable entanglement swapping: Highly correlated four-partite quantum state,” Phys. Rev. A 68, 012319 (2003).
[Crossref]

Martinelli, M.

Mattle, K.

D. Bouwmeester, J.W. Pan, K. Mattle, M. Eibl, H Weinfurter, and A. Zeilinger, “Experimental quantum teleportation,” Nature 390, 575–579 (1997).
[Crossref]

K. Mattle, H. Weinfurter, P. G. Kwiat, and A. Zeilinger, “Dense coding in experimental quantum communications,” Phys. Rev. Lett. 76, 4656–4659 (1996).
[Crossref] [PubMed]

P. G. Kwiat, K. Mattle, H Weinfurter, A. Zeilinger, A. V. Sergienko, and Y. Shih, “New high-intensity source of polarization-entangled photon pairs,” Phys. Rev. Lett. 75, 4337–4341 (1995).
[Crossref] [PubMed]

McKinstrie, C. J.

C. J. McKinstrie, S. Radic, M. G. Raymer, and L. Schenato, “Unimpaired phase-sensitive amplification by vector four-wave mixing near the zero-dispersion frequency,” Opt. Express 15, 2178–2189 (2007).
[Crossref] [PubMed]

C. J. McKinstrie and M. G. Raymer, “Four-wave mixing cascades near the zero-dispersion frequency,” Opt. Express 14, 9600–9610 (2006).
[Crossref] [PubMed]

C. J. McKinstrie, J. D. Harvey, S. Radic, and M. G. Raymer, “Translation of quantum states by four-wave mixing in fibers,” Opt. Express 13, 9131–9142 (2005).
[Crossref] [PubMed]

C. J. McKinstrie, M. Yu, M. G. Raymer, and S. Radic, “Quantum noise properties of parametric processes in fibers,” Opt. Express 13, 4986–5012 (2005).
[Crossref] [PubMed]

C. J. McKinstrie and S. Radic, “Phase-sensitive amplification in a fiber,” Opt. Express 12, 4973–4979 (2004).
[Crossref] [PubMed]

C. J. McKinstrie, S. Radic, and M. G. Raymer, “Quantum noise properties of parametric amplifiers driven by two pump waves,” Opt. Express 12, 5037–5066 (2004).
[Crossref] [PubMed]

S. Radic, C. J. McKinstrie, R. M. Jopson, J. C. Centanni, Q. Lin, and G. P. Agrawal, “Record performance of a parametric amplifier constructed with highly-nonlinear fiber,” Electron. Lett. 39, 838–839 (2003).
[Crossref]

C. J. McKinstrie, S. Radic, and C. Xie, “Parametric instabilities driven by orthogonal pump waves in birefringent fibers,” Opt. Express 11, 2619–2633 (2003).
[Crossref] [PubMed]

C. J. McKinstrie, S. Radic, and A. R. Chraplyvy, “Parametric amplifiers driven by two pump waves,” IEEE J. Sel. Top. Quantum Electron. 8, 538–547 and 956 (2002).
[Crossref]

Menicucci, N. C.

N. C. Menicucci, P. van Loock, M. Gu, C. Weedbrook, T. C. Ralph, and M. A. Nielsen, “Universal quantum computation with continuous-variable cluster states,” Phys. Rev. Lett. 97, 110501 (2006).
[Crossref] [PubMed]

Migdall, A.

Naik, D. S.

D. S. Naik, C. G. Peterson, A. G. White, A. J. Berglund, and P. G. Kwiat, “Entangled state quantum cryptography: Eavesdropping on the Ekert protocol,” Phys. Rev. Lett. 84, 4733–4736 (2000).
[Crossref] [PubMed]

Nielsen, M. A.

N. C. Menicucci, P. van Loock, M. Gu, C. Weedbrook, T. C. Ralph, and M. A. Nielsen, “Universal quantum computation with continuous-variable cluster states,” Phys. Rev. Lett. 97, 110501 (2006).
[Crossref] [PubMed]

M. A. Nielsen, “Optical quantum computing using cluster states,” Phys. Rev. Lett. 93, 040503 (2004).
[Crossref] [PubMed]

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

Nussenzveig, P.

Pan, J. W.

J. W. Pan, M. Daniell, S. Gasparoni, G. Weihs, and A. Zeilinger, “Experimental demonstration of four-photon entanglement and high-fidelity teleportation,” Phys. Rev. Lett. 86, 4435–4438 (2001).
[Crossref] [PubMed]

D. Bouwmeester, J. W. Pan, M. Daniell, H. Weinfurter, and A. Zeilinger, “Observation of three-photon Greenburger-Horne-Zeilinger entanglement,” Phys. Rev. Lett. 82, 1345–1349 (1999).
[Crossref]

Pan, J.W.

D. Bouwmeester, J.W. Pan, K. Mattle, M. Eibl, H Weinfurter, and A. Zeilinger, “Experimental quantum teleportation,” Nature 390, 575–579 (1997).
[Crossref]

Pan, Q.

O. Glöckl, S. Lorenz, C. Marquardt, J. Heersink, M. Brownnutt, C. Silberhorn, Q. Pan, P. van Loock, N. Korolkova, and G. Leuchs, “Experiment towards continuous-variable entanglement swapping: Highly correlated four-partite quantum state,” Phys. Rev. A 68, 012319 (2003).
[Crossref]

X. Li, Q. Pan, J. Jing, J. Zhang, C. Xie, and K. Peng, “Quantum dense coding exploiting a bright Einstein-Podolsky-Rosen beam,” Phys. Rev. Lett. 88, 047904 (2002).
[Crossref] [PubMed]

Paris, M. G. A.

Pati, A. K.

S. L. Braunstein and A. K. Pati, Quantum Information with Continuous Variables (Kluwer Academic Press, 2003).

Peng, K.

X. Su, A. Tan, X. Jia, J. Zhang, C. Xie, and K. Peng, “Experimental preparation of quadripartite cluster and Greenberger-Horne-Zeilinger entangled states for continuous variables,” Phys. Rev. Lett. 98, 707502 (2007).
[Crossref]

J. Jing, J. Zhang, Y. Fan, F. Zhao, C. Xie, and K. Peng, “Experimental demonstration of tripartite entanglement and controlled dense coding for continuous variables,” Phys. Rev. Lett. 90, 167903 (2003).
[Crossref] [PubMed]

X. Li, Q. Pan, J. Jing, J. Zhang, C. Xie, and K. Peng, “Quantum dense coding exploiting a bright Einstein-Podolsky-Rosen beam,” Phys. Rev. Lett. 88, 047904 (2002).
[Crossref] [PubMed]

J. Zhang, C. Xie, and K. Peng, “Controlled dense coding for continuous variables using three-partite entangled states,” Phys. Rev. A 66, 032318 (2002).
[Crossref]

Peres, A.

C. H. Bennett, G. Brassard, C. Crepeau, R. Josza, A. Peres, and W. K. Wootters, “Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels,” Phys. Rev. Lett. 70, 1895–1899 (1993).
[Crossref] [PubMed]

Peterson, C. G.

D. S. Naik, C. G. Peterson, A. G. White, A. J. Berglund, and P. G. Kwiat, “Entangled state quantum cryptography: Eavesdropping on the Ekert protocol,” Phys. Rev. Lett. 84, 4733–4736 (2000).
[Crossref] [PubMed]

Pfister, O.

R. C. Pooser and O. Pfister, “Observation of triply coincident nonlinearities in periodically poled KTiOPO4,” Opt. Lett. 30, 2635–2637 (2005).
[Crossref] [PubMed]

O. Pfister, S. Feng, G. Jennings, R. Pooser, and D. Xie, “Multipartite continuous-variable entanglement from concurrent nonlinearities,” Phys. Rev. A 70, 020302R (2004).
[Crossref]

Polzik, E. S.

A. Furusawa, J. L. Sorensen, S. J. Braunstein, C. A. Fuchs, H. J. Kimble, and E. S. Polzik, “Unconditional quantum teleportation,” Science 282, 706–709 (1998).
[Crossref] [PubMed]

Pooser, R.

O. Pfister, S. Feng, G. Jennings, R. Pooser, and D. Xie, “Multipartite continuous-variable entanglement from concurrent nonlinearities,” Phys. Rev. A 70, 020302R (2004).
[Crossref]

Pooser, R. C.

Puddu, E.

Radic, S.

C. J. McKinstrie, S. Radic, M. G. Raymer, and L. Schenato, “Unimpaired phase-sensitive amplification by vector four-wave mixing near the zero-dispersion frequency,” Opt. Express 15, 2178–2189 (2007).
[Crossref] [PubMed]

C. J. McKinstrie, M. Yu, M. G. Raymer, and S. Radic, “Quantum noise properties of parametric processes in fibers,” Opt. Express 13, 4986–5012 (2005).
[Crossref] [PubMed]

C. J. McKinstrie, J. D. Harvey, S. Radic, and M. G. Raymer, “Translation of quantum states by four-wave mixing in fibers,” Opt. Express 13, 9131–9142 (2005).
[Crossref] [PubMed]

C. J. McKinstrie, S. Radic, and M. G. Raymer, “Quantum noise properties of parametric amplifiers driven by two pump waves,” Opt. Express 12, 5037–5066 (2004).
[Crossref] [PubMed]

C. J. McKinstrie and S. Radic, “Phase-sensitive amplification in a fiber,” Opt. Express 12, 4973–4979 (2004).
[Crossref] [PubMed]

C. J. McKinstrie, S. Radic, and C. Xie, “Parametric instabilities driven by orthogonal pump waves in birefringent fibers,” Opt. Express 11, 2619–2633 (2003).
[Crossref] [PubMed]

S. Radic, C. J. McKinstrie, R. M. Jopson, J. C. Centanni, Q. Lin, and G. P. Agrawal, “Record performance of a parametric amplifier constructed with highly-nonlinear fiber,” Electron. Lett. 39, 838–839 (2003).
[Crossref]

C. J. McKinstrie, S. Radic, and A. R. Chraplyvy, “Parametric amplifiers driven by two pump waves,” IEEE J. Sel. Top. Quantum Electron. 8, 538–547 and 956 (2002).
[Crossref]

Radmore, P. M.

S. M. Barnett and P. M. Radmore, Methods in Theoretical Quantum Optics (Oxford University Press, 1997).

Ralph, T. C.

N. C. Menicucci, P. van Loock, M. Gu, C. Weedbrook, T. C. Ralph, and M. A. Nielsen, “Universal quantum computation with continuous-variable cluster states,” Phys. Rev. Lett. 97, 110501 (2006).
[Crossref] [PubMed]

W. P. Bowen, N. Treps, B. C. Buchler, R. Schnabel, T. C. Ralph, H. A. Bachor, T. Symul, and P. K. Lam, “Experimental investigation of continuous-variable quantum teleportation,” Phys. Rev. A 67, 032302 (2003).
[Crossref]

Rarity, J. G.

Raussendorf, R.

R. Raussendorf and H. J. Briegel, “A one-way quantum computer,” Phys. Rev. Lett. 86, 5188–5191 (2001).
[Crossref] [PubMed]

Raymer, M. G.

Reeves, W. H.

Resch, K. J.

P. Walther, K. J. Resch, T. Rudolph, E. Schenk, H. Weinfurter, V. Vedral, M. Aspelmeyer, and A. Zeilinger, “Experimental one-way quantum computing,” Nature 434, 169–176 (2005).
[Crossref] [PubMed]

Roberts, P. J.

Rodionov, A. V.

A. V. Rodionov and A. S. Chirkin, “Entangled photon states in consecutive nonlinear optical interactions,” JETP Lett. 79, 253–256 and 582 (2004).
[Crossref]

Rowe, H. E.

J.M Manley and H. E. Rowe, “Some general properties of nonlinear elements—Part I. General energy relations,” Proc. IRE 44, 904–913 (1956).
[Crossref]

Rudolph, T.

P. Walther, K. J. Resch, T. Rudolph, E. Schenk, H. Weinfurter, V. Vedral, M. Aspelmeyer, and A. Zeilinger, “Experimental one-way quantum computing,” Nature 434, 169–176 (2005).
[Crossref] [PubMed]

Russell, P. S. J.

Sanders, B. C.

A. M. Lance, T. Symul, W. P. Bowen, B. C. Sanders, and P. K. Lam, “Tripartite quantum state sharing,” Phys. Rev. Lett. 92, 177903 (2004).
[Crossref] [PubMed]

Schenato, L.

Schenk, E.

P. Walther, K. J. Resch, T. Rudolph, E. Schenk, H. Weinfurter, V. Vedral, M. Aspelmeyer, and A. Zeilinger, “Experimental one-way quantum computing,” Nature 434, 169–176 (2005).
[Crossref] [PubMed]

Schmid, C.

N. Kiesel, C. Schmid, U. Weber, G. Toth, O. Guhne, R. Ursin, and H. Weinfurter, “Experimental analysis of a four-qubit photon cluster state,” Phys. Rev. Lett. 95, 210502 (2005).
[Crossref] [PubMed]

Schnabel, R.

W. P. Bowen, N. Treps, B. C. Buchler, R. Schnabel, T. C. Ralph, H. A. Bachor, T. Symul, and P. K. Lam, “Experimental investigation of continuous-variable quantum teleportation,” Phys. Rev. A 67, 032302 (2003).
[Crossref]

Schrödinger, E.

E. Schrödinger, “Die gegenwärtige Situation in der Quantenmechanik,” Naturwiss. 28, 807–812, 823–828 and 844–849 (1928).

Sergienko, A. V.

P. G. Kwiat, K. Mattle, H Weinfurter, A. Zeilinger, A. V. Sergienko, and Y. Shih, “New high-intensity source of polarization-entangled photon pairs,” Phys. Rev. Lett. 75, 4337–4341 (1995).
[Crossref] [PubMed]

Sharping, J. E.

J. E. Sharping, J. Chen, X. Li, and P. Kumar, “Quantum-correlated twin photons from microstructure fiber,” Opt. Express 12, 3086–3094 (2004).
[Crossref] [PubMed]

M. Fiorentino, P. L. Voss, J. E. Sharping, and P. Kumar, “All-fiber photon-pair source for quantum communications,” IEEE Photon. Technol. Lett. 14, 983–985 (2002).
[Crossref]

Shih, Y.

P. G. Kwiat, K. Mattle, H Weinfurter, A. Zeilinger, A. V. Sergienko, and Y. Shih, “New high-intensity source of polarization-entangled photon pairs,” Phys. Rev. Lett. 75, 4337–4341 (1995).
[Crossref] [PubMed]

Silberhorn, C.

O. Glöckl, S. Lorenz, C. Marquardt, J. Heersink, M. Brownnutt, C. Silberhorn, Q. Pan, P. van Loock, N. Korolkova, and G. Leuchs, “Experiment towards continuous-variable entanglement swapping: Highly correlated four-partite quantum state,” Phys. Rev. A 68, 012319 (2003).
[Crossref]

Simon, C.

T. Jennewein, C. Simon, G. Weihs, H. Weinfurter, and A. Zeilinger, “Quantum cryptography with entangled photons,” Phys. Rev. Lett. 84, 4729–4732 (2000).
[Crossref] [PubMed]

Sorensen, J. L.

A. Furusawa, J. L. Sorensen, S. J. Braunstein, C. A. Fuchs, H. J. Kimble, and E. S. Polzik, “Unconditional quantum teleportation,” Science 282, 706–709 (1998).
[Crossref] [PubMed]

Su, X.

X. Su, A. Tan, X. Jia, J. Zhang, C. Xie, and K. Peng, “Experimental preparation of quadripartite cluster and Greenberger-Horne-Zeilinger entangled states for continuous variables,” Phys. Rev. Lett. 98, 707502 (2007).
[Crossref]

Sun, F. G.

Z. G. Lu, P. J. Bock, J. R. Liu, F. G. Sun, and T. J. Hall, “All-optical 1550 to 1310 nm wavelength converter,” Electron. Lett. 42, 937–938 (2006).
[Crossref]

Symul, T.

A. M. Lance, T. Symul, W. P. Bowen, B. C. Sanders, and P. K. Lam, “Tripartite quantum state sharing,” Phys. Rev. Lett. 92, 177903 (2004).
[Crossref] [PubMed]

W. P. Bowen, N. Treps, B. C. Buchler, R. Schnabel, T. C. Ralph, H. A. Bachor, T. Symul, and P. K. Lam, “Experimental investigation of continuous-variable quantum teleportation,” Phys. Rev. A 67, 032302 (2003).
[Crossref]

Takei, N.

T. Aoki, N. Takei, H. Yonezawa, K. Wakui, T. Hiraoka, and A. Furusawa, “Experimental creation of a fully inseparable tripartite continuous-variable state,” Phys. Rev. Lett. 91, 080404 (2003).
[Crossref] [PubMed]

Takesue, H.

H. Takesue and K. Inoue, “Generation of polarization-entangled photon pairs and violation of Bell’s inequality using spontaneous four-wave mixing in a fiber loop,” Phys. Rev. A 70, 031802R (2004).
[Crossref]

Tan, A.

X. Su, A. Tan, X. Jia, J. Zhang, C. Xie, and K. Peng, “Experimental preparation of quadripartite cluster and Greenberger-Horne-Zeilinger entangled states for continuous variables,” Phys. Rev. Lett. 98, 707502 (2007).
[Crossref]

Tittel, W.

W. Tittel, J. Brendel, H. Zbinden, and N. Gisin, “Quantum cryptography using entangled photons in energy-time Bell states,” Phys. Rev. Lett. 84, 4737–4740 (2000).
[Crossref] [PubMed]

Toth, G.

N. Kiesel, C. Schmid, U. Weber, G. Toth, O. Guhne, R. Ursin, and H. Weinfurter, “Experimental analysis of a four-qubit photon cluster state,” Phys. Rev. Lett. 95, 210502 (2005).
[Crossref] [PubMed]

Treps, N.

W. P. Bowen, N. Treps, B. C. Buchler, R. Schnabel, T. C. Ralph, H. A. Bachor, T. Symul, and P. K. Lam, “Experimental investigation of continuous-variable quantum teleportation,” Phys. Rev. A 67, 032302 (2003).
[Crossref]

Ursin, R.

N. Kiesel, C. Schmid, U. Weber, G. Toth, O. Guhne, R. Ursin, and H. Weinfurter, “Experimental analysis of a four-qubit photon cluster state,” Phys. Rev. Lett. 95, 210502 (2005).
[Crossref] [PubMed]

Valente, P.

van Enk, S. J.

S. J. van Enk, “Entanglement of electromagnetic fields,” Phys. Rev. A 67, 022303 (2003).
[Crossref]

van Loock, P.

N. C. Menicucci, P. van Loock, M. Gu, C. Weedbrook, T. C. Ralph, and M. A. Nielsen, “Universal quantum computation with continuous-variable cluster states,” Phys. Rev. Lett. 97, 110501 (2006).
[Crossref] [PubMed]

O. Glöckl, S. Lorenz, C. Marquardt, J. Heersink, M. Brownnutt, C. Silberhorn, Q. Pan, P. van Loock, N. Korolkova, and G. Leuchs, “Experiment towards continuous-variable entanglement swapping: Highly correlated four-partite quantum state,” Phys. Rev. A 68, 012319 (2003).
[Crossref]

P. van Loock and A. Furusawa, “Detecting genuine multipartite continuous-variable entanglement,” Phys. Rev. A 67, 052315 (2003).
[Crossref]

P. van Loock and S. L. Braunstein, “Multipartite entanglement for continuous variables: A quantum teleportation network,” Phys. Rev. Lett. 84, 3482–3485 (2000).
[Crossref] [PubMed]

Varizi, A.

S. Gröblacher, T. Jennewein, A. Varizi, G. Weihs, and A. Zeilinger, “Experimental quantum cryptography with qutrits,” New J. Phys. 8, 75 (2006).
[Crossref]

Vedral, V.

P. Walther, K. J. Resch, T. Rudolph, E. Schenk, H. Weinfurter, V. Vedral, M. Aspelmeyer, and A. Zeilinger, “Experimental one-way quantum computing,” Nature 434, 169–176 (2005).
[Crossref] [PubMed]

Villar, A. S.

Voss, P. L.

M. Fiorentino, P. L. Voss, J. E. Sharping, and P. Kumar, “All-fiber photon-pair source for quantum communications,” IEEE Photon. Technol. Lett. 14, 983–985 (2002).
[Crossref]

Wadsworth, W. J.

Wakui, K.

T. Aoki, N. Takei, H. Yonezawa, K. Wakui, T. Hiraoka, and A. Furusawa, “Experimental creation of a fully inseparable tripartite continuous-variable state,” Phys. Rev. Lett. 91, 080404 (2003).
[Crossref] [PubMed]

Walther, P.

P. Walther, K. J. Resch, T. Rudolph, E. Schenk, H. Weinfurter, V. Vedral, M. Aspelmeyer, and A. Zeilinger, “Experimental one-way quantum computing,” Nature 434, 169–176 (2005).
[Crossref] [PubMed]

Weber, U.

N. Kiesel, C. Schmid, U. Weber, G. Toth, O. Guhne, R. Ursin, and H. Weinfurter, “Experimental analysis of a four-qubit photon cluster state,” Phys. Rev. Lett. 95, 210502 (2005).
[Crossref] [PubMed]

Weedbrook, C.

N. C. Menicucci, P. van Loock, M. Gu, C. Weedbrook, T. C. Ralph, and M. A. Nielsen, “Universal quantum computation with continuous-variable cluster states,” Phys. Rev. Lett. 97, 110501 (2006).
[Crossref] [PubMed]

Weihs, G.

S. Gröblacher, T. Jennewein, A. Varizi, G. Weihs, and A. Zeilinger, “Experimental quantum cryptography with qutrits,” New J. Phys. 8, 75 (2006).
[Crossref]

J. W. Pan, M. Daniell, S. Gasparoni, G. Weihs, and A. Zeilinger, “Experimental demonstration of four-photon entanglement and high-fidelity teleportation,” Phys. Rev. Lett. 86, 4435–4438 (2001).
[Crossref] [PubMed]

T. Jennewein, C. Simon, G. Weihs, H. Weinfurter, and A. Zeilinger, “Quantum cryptography with entangled photons,” Phys. Rev. Lett. 84, 4729–4732 (2000).
[Crossref] [PubMed]

Weinberg, D. L.

D. C. Burnham and D. L. Weinberg, “Observation of simultaneity in parametric production of optical photon pairs,” Phys. Rev. Lett. 25, 84–87 (1970).
[Crossref]

Weinfurter, H

D. Bouwmeester, J.W. Pan, K. Mattle, M. Eibl, H Weinfurter, and A. Zeilinger, “Experimental quantum teleportation,” Nature 390, 575–579 (1997).
[Crossref]

P. G. Kwiat, K. Mattle, H Weinfurter, A. Zeilinger, A. V. Sergienko, and Y. Shih, “New high-intensity source of polarization-entangled photon pairs,” Phys. Rev. Lett. 75, 4337–4341 (1995).
[Crossref] [PubMed]

Weinfurter, H.

N. Kiesel, C. Schmid, U. Weber, G. Toth, O. Guhne, R. Ursin, and H. Weinfurter, “Experimental analysis of a four-qubit photon cluster state,” Phys. Rev. Lett. 95, 210502 (2005).
[Crossref] [PubMed]

P. Walther, K. J. Resch, T. Rudolph, E. Schenk, H. Weinfurter, V. Vedral, M. Aspelmeyer, and A. Zeilinger, “Experimental one-way quantum computing,” Nature 434, 169–176 (2005).
[Crossref] [PubMed]

T. Jennewein, C. Simon, G. Weihs, H. Weinfurter, and A. Zeilinger, “Quantum cryptography with entangled photons,” Phys. Rev. Lett. 84, 4729–4732 (2000).
[Crossref] [PubMed]

D. Bouwmeester, J. W. Pan, M. Daniell, H. Weinfurter, and A. Zeilinger, “Observation of three-photon Greenburger-Horne-Zeilinger entanglement,” Phys. Rev. Lett. 82, 1345–1349 (1999).
[Crossref]

K. Mattle, H. Weinfurter, P. G. Kwiat, and A. Zeilinger, “Dense coding in experimental quantum communications,” Phys. Rev. Lett. 76, 4656–4659 (1996).
[Crossref] [PubMed]

Weiss, M. T.

M. T. Weiss, “Quantum derivation of energy relations analogous to those for nonlinear rectances,” Proc. IRE 45, 1012–1013 (1957).

White, A. G.

D. S. Naik, C. G. Peterson, A. G. White, A. J. Berglund, and P. G. Kwiat, “Entangled state quantum cryptography: Eavesdropping on the Ekert protocol,” Phys. Rev. Lett. 84, 4733–4736 (2000).
[Crossref] [PubMed]

Wiesner, S. J.

C. H. Bennett and S. J. Wiesner, “Communication via one- and two-particle operators on Einstein-Podolsky-Rosen states,” Phys. Rev. Lett. 69, 2881–2884 (1992).
[Crossref] [PubMed]

Wootters, W. K.

C. H. Bennett, G. Brassard, C. Crepeau, R. Josza, A. Peres, and W. K. Wootters, “Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels,” Phys. Rev. Lett. 70, 1895–1899 (1993).
[Crossref] [PubMed]

Wu, H.

L. A. Wu, H. J. Kimble, J. L. Hall, and H. Wu, “Generation of squeezed states by parametric down conversion,” Phys. Rev. Lett. 57, 2520–2523 (1986).
[Crossref] [PubMed]

Wu, L. A.

L. A. Wu, H. J. Kimble, J. L. Hall, and H. Wu, “Generation of squeezed states by parametric down conversion,” Phys. Rev. Lett. 57, 2520–2523 (1986).
[Crossref] [PubMed]

Xie, C.

X. Su, A. Tan, X. Jia, J. Zhang, C. Xie, and K. Peng, “Experimental preparation of quadripartite cluster and Greenberger-Horne-Zeilinger entangled states for continuous variables,” Phys. Rev. Lett. 98, 707502 (2007).
[Crossref]

C. J. McKinstrie, S. Radic, and C. Xie, “Parametric instabilities driven by orthogonal pump waves in birefringent fibers,” Opt. Express 11, 2619–2633 (2003).
[Crossref] [PubMed]

J. Jing, J. Zhang, Y. Fan, F. Zhao, C. Xie, and K. Peng, “Experimental demonstration of tripartite entanglement and controlled dense coding for continuous variables,” Phys. Rev. Lett. 90, 167903 (2003).
[Crossref] [PubMed]

X. Li, Q. Pan, J. Jing, J. Zhang, C. Xie, and K. Peng, “Quantum dense coding exploiting a bright Einstein-Podolsky-Rosen beam,” Phys. Rev. Lett. 88, 047904 (2002).
[Crossref] [PubMed]

J. Zhang, C. Xie, and K. Peng, “Controlled dense coding for continuous variables using three-partite entangled states,” Phys. Rev. A 66, 032318 (2002).
[Crossref]

Xie, D.

O. Pfister, S. Feng, G. Jennings, R. Pooser, and D. Xie, “Multipartite continuous-variable entanglement from concurrent nonlinearities,” Phys. Rev. A 70, 020302R (2004).
[Crossref]

Yonezawa, H.

H. Yonezawa, T. Aoki, and A. Furusawa, “Demonstration of a quantum teleportation network for continuous variabes,” Nature 431, 430–434 (2004).
[Crossref] [PubMed]

T. Aoki, N. Takei, H. Yonezawa, K. Wakui, T. Hiraoka, and A. Furusawa, “Experimental creation of a fully inseparable tripartite continuous-variable state,” Phys. Rev. Lett. 91, 080404 (2003).
[Crossref] [PubMed]

Yu, M.

Zbinden, H.

W. Tittel, J. Brendel, H. Zbinden, and N. Gisin, “Quantum cryptography using entangled photons in energy-time Bell states,” Phys. Rev. Lett. 84, 4737–4740 (2000).
[Crossref] [PubMed]

Zeilinger, A.

S. Gröblacher, T. Jennewein, A. Varizi, G. Weihs, and A. Zeilinger, “Experimental quantum cryptography with qutrits,” New J. Phys. 8, 75 (2006).
[Crossref]

P. Walther, K. J. Resch, T. Rudolph, E. Schenk, H. Weinfurter, V. Vedral, M. Aspelmeyer, and A. Zeilinger, “Experimental one-way quantum computing,” Nature 434, 169–176 (2005).
[Crossref] [PubMed]

J. W. Pan, M. Daniell, S. Gasparoni, G. Weihs, and A. Zeilinger, “Experimental demonstration of four-photon entanglement and high-fidelity teleportation,” Phys. Rev. Lett. 86, 4435–4438 (2001).
[Crossref] [PubMed]

T. Jennewein, C. Simon, G. Weihs, H. Weinfurter, and A. Zeilinger, “Quantum cryptography with entangled photons,” Phys. Rev. Lett. 84, 4729–4732 (2000).
[Crossref] [PubMed]

D. Bouwmeester, J. W. Pan, M. Daniell, H. Weinfurter, and A. Zeilinger, “Observation of three-photon Greenburger-Horne-Zeilinger entanglement,” Phys. Rev. Lett. 82, 1345–1349 (1999).
[Crossref]

D. Bouwmeester, J.W. Pan, K. Mattle, M. Eibl, H Weinfurter, and A. Zeilinger, “Experimental quantum teleportation,” Nature 390, 575–579 (1997).
[Crossref]

K. Mattle, H. Weinfurter, P. G. Kwiat, and A. Zeilinger, “Dense coding in experimental quantum communications,” Phys. Rev. Lett. 76, 4656–4659 (1996).
[Crossref] [PubMed]

P. G. Kwiat, K. Mattle, H Weinfurter, A. Zeilinger, A. V. Sergienko, and Y. Shih, “New high-intensity source of polarization-entangled photon pairs,” Phys. Rev. Lett. 75, 4337–4341 (1995).
[Crossref] [PubMed]

Zhang, J.

X. Su, A. Tan, X. Jia, J. Zhang, C. Xie, and K. Peng, “Experimental preparation of quadripartite cluster and Greenberger-Horne-Zeilinger entangled states for continuous variables,” Phys. Rev. Lett. 98, 707502 (2007).
[Crossref]

J. Jing, J. Zhang, Y. Fan, F. Zhao, C. Xie, and K. Peng, “Experimental demonstration of tripartite entanglement and controlled dense coding for continuous variables,” Phys. Rev. Lett. 90, 167903 (2003).
[Crossref] [PubMed]

J. Zhang, C. Xie, and K. Peng, “Controlled dense coding for continuous variables using three-partite entangled states,” Phys. Rev. A 66, 032318 (2002).
[Crossref]

X. Li, Q. Pan, J. Jing, J. Zhang, C. Xie, and K. Peng, “Quantum dense coding exploiting a bright Einstein-Podolsky-Rosen beam,” Phys. Rev. Lett. 88, 047904 (2002).
[Crossref] [PubMed]

Zhang, T. C.

T. C. Zhang, K. W. Goh, C. W. Chou, P. Lodahl, and H. J. Kimble, “Quantum teleportation of light beams,” Phys. Rev. A 67, 033802 (2003).
[Crossref]

Zhao, F.

J. Jing, J. Zhang, Y. Fan, F. Zhao, C. Xie, and K. Peng, “Experimental demonstration of tripartite entanglement and controlled dense coding for continuous variables,” Phys. Rev. Lett. 90, 167903 (2003).
[Crossref] [PubMed]

Electron. Lett. (2)

S. Radic, C. J. McKinstrie, R. M. Jopson, J. C. Centanni, Q. Lin, and G. P. Agrawal, “Record performance of a parametric amplifier constructed with highly-nonlinear fiber,” Electron. Lett. 39, 838–839 (2003).
[Crossref]

Z. G. Lu, P. J. Bock, J. R. Liu, F. G. Sun, and T. J. Hall, “All-optical 1550 to 1310 nm wavelength converter,” Electron. Lett. 42, 937–938 (2006).
[Crossref]

IEEE J. Sel. Top. Quantum Electron. (1)

C. J. McKinstrie, S. Radic, and A. R. Chraplyvy, “Parametric amplifiers driven by two pump waves,” IEEE J. Sel. Top. Quantum Electron. 8, 538–547 and 956 (2002).
[Crossref]

IEEE Photon. Technol. Lett. (1)

M. Fiorentino, P. L. Voss, J. E. Sharping, and P. Kumar, “All-fiber photon-pair source for quantum communications,” IEEE Photon. Technol. Lett. 14, 983–985 (2002).
[Crossref]

J. Opt. Soc. Am. B (1)

JETP Lett. (1)

A. V. Rodionov and A. S. Chirkin, “Entangled photon states in consecutive nonlinear optical interactions,” JETP Lett. 79, 253–256 and 582 (2004).
[Crossref]

Nature (3)

D. Bouwmeester, J.W. Pan, K. Mattle, M. Eibl, H Weinfurter, and A. Zeilinger, “Experimental quantum teleportation,” Nature 390, 575–579 (1997).
[Crossref]

H. Yonezawa, T. Aoki, and A. Furusawa, “Demonstration of a quantum teleportation network for continuous variabes,” Nature 431, 430–434 (2004).
[Crossref] [PubMed]

P. Walther, K. J. Resch, T. Rudolph, E. Schenk, H. Weinfurter, V. Vedral, M. Aspelmeyer, and A. Zeilinger, “Experimental one-way quantum computing,” Nature 434, 169–176 (2005).
[Crossref] [PubMed]

Naturwiss. (1)

E. Schrödinger, “Die gegenwärtige Situation in der Quantenmechanik,” Naturwiss. 28, 807–812, 823–828 and 844–849 (1928).

New J. Phys. (1)

S. Gröblacher, T. Jennewein, A. Varizi, G. Weihs, and A. Zeilinger, “Experimental quantum cryptography with qutrits,” New J. Phys. 8, 75 (2006).
[Crossref]

Opt. Express (13)

J. E. Sharping, J. Chen, X. Li, and P. Kumar, “Quantum-correlated twin photons from microstructure fiber,” Opt. Express 12, 3086–3094 (2004).
[Crossref] [PubMed]

M. Bondani, A. Allevi, E. Gevinti, A. Agliati, and A. Andreoni, “3D phase-matching conditions for the generation of entangled triplets by χ(2) interlinked interactions,” Opt. Express 14, 9838–9843 (2006).
[Crossref] [PubMed]

C. J. McKinstrie, S. Radic, and C. Xie, “Parametric instabilities driven by orthogonal pump waves in birefringent fibers,” Opt. Express 11, 2619–2633 (2003).
[Crossref] [PubMed]

C. J. McKinstrie, S. Radic, and M. G. Raymer, “Quantum noise properties of parametric amplifiers driven by two pump waves,” Opt. Express 12, 5037–5066 (2004).
[Crossref] [PubMed]

C. J. McKinstrie and M. G. Raymer, “Four-wave mixing cascades near the zero-dispersion frequency,” Opt. Express 14, 9600–9610 (2006).
[Crossref] [PubMed]

C. J. McKinstrie, S. Radic, M. G. Raymer, and L. Schenato, “Unimpaired phase-sensitive amplification by vector four-wave mixing near the zero-dispersion frequency,” Opt. Express 15, 2178–2189 (2007).
[Crossref] [PubMed]

C. J. McKinstrie and S. Radic, “Phase-sensitive amplification in a fiber,” Opt. Express 12, 4973–4979 (2004).
[Crossref] [PubMed]

J. Fan and A. Migdall, “Generation of cross-polarized photon pairs in a microstructure fiber with frequency-conjugate laser pump pulses,” Opt. Express 13, 5777–5782 (2005).
[Crossref] [PubMed]

W. H. Reeves, J. C. Knight, P. S. J. Russell, and P. J. Roberts, “Demonstration of ultra-flattened dispersion in photonic crystal fibers,” Opt. Express 10, 609–613 (2002).
[PubMed]

K. P. Hansen, “Dispersion flattened hybrid-core nonlinear photonic crystal fiber,” Opt. Express 11, 1503–1509 (2003).
[Crossref] [PubMed]

J. G. Rarity, J. Fulconis, J. Duligall, W. J. Wadsworth, and P. S. J. Russell, “Photonic crystal fiber source of correlated photon pairs,” Opt. Express 13, 534–544 (2005).
[Crossref] [PubMed]

C. J. McKinstrie, J. D. Harvey, S. Radic, and M. G. Raymer, “Translation of quantum states by four-wave mixing in fibers,” Opt. Express 13, 9131–9142 (2005).
[Crossref] [PubMed]

C. J. McKinstrie, M. Yu, M. G. Raymer, and S. Radic, “Quantum noise properties of parametric processes in fibers,” Opt. Express 13, 4986–5012 (2005).
[Crossref] [PubMed]

Opt. Lett. (2)

Phys. Rev. A (9)

H. Takesue and K. Inoue, “Generation of polarization-entangled photon pairs and violation of Bell’s inequality using spontaneous four-wave mixing in a fiber loop,” Phys. Rev. A 70, 031802R (2004).
[Crossref]

P. van Loock and A. Furusawa, “Detecting genuine multipartite continuous-variable entanglement,” Phys. Rev. A 67, 052315 (2003).
[Crossref]

S. J. van Enk, “Entanglement of electromagnetic fields,” Phys. Rev. A 67, 022303 (2003).
[Crossref]

J. Zhang, C. Xie, and K. Peng, “Controlled dense coding for continuous variables using three-partite entangled states,” Phys. Rev. A 66, 032318 (2002).
[Crossref]

S. L. Braunstein and H. J. Kimble, “Dense coding for continuous variables,” Phys. Rev. A 61, 042302 (2000).
[Crossref]

W. P. Bowen, N. Treps, B. C. Buchler, R. Schnabel, T. C. Ralph, H. A. Bachor, T. Symul, and P. K. Lam, “Experimental investigation of continuous-variable quantum teleportation,” Phys. Rev. A 67, 032302 (2003).
[Crossref]

T. C. Zhang, K. W. Goh, C. W. Chou, P. Lodahl, and H. J. Kimble, “Quantum teleportation of light beams,” Phys. Rev. A 67, 033802 (2003).
[Crossref]

O. Pfister, S. Feng, G. Jennings, R. Pooser, and D. Xie, “Multipartite continuous-variable entanglement from concurrent nonlinearities,” Phys. Rev. A 70, 020302R (2004).
[Crossref]

O. Glöckl, S. Lorenz, C. Marquardt, J. Heersink, M. Brownnutt, C. Silberhorn, Q. Pan, P. van Loock, N. Korolkova, and G. Leuchs, “Experiment towards continuous-variable entanglement swapping: Highly correlated four-partite quantum state,” Phys. Rev. A 68, 012319 (2003).
[Crossref]

Phys. Rev. Lett. (23)

X. Su, A. Tan, X. Jia, J. Zhang, C. Xie, and K. Peng, “Experimental preparation of quadripartite cluster and Greenberger-Horne-Zeilinger entangled states for continuous variables,” Phys. Rev. Lett. 98, 707502 (2007).
[Crossref]

D. C. Burnham and D. L. Weinberg, “Observation of simultaneity in parametric production of optical photon pairs,” Phys. Rev. Lett. 25, 84–87 (1970).
[Crossref]

P. G. Kwiat, K. Mattle, H Weinfurter, A. Zeilinger, A. V. Sergienko, and Y. Shih, “New high-intensity source of polarization-entangled photon pairs,” Phys. Rev. Lett. 75, 4337–4341 (1995).
[Crossref] [PubMed]

L. A. Wu, H. J. Kimble, J. L. Hall, and H. Wu, “Generation of squeezed states by parametric down conversion,” Phys. Rev. Lett. 57, 2520–2523 (1986).
[Crossref] [PubMed]

S. L. Braunstein and H. J. Kimble, “Teleportation of continuous quantum variables,” Phys. Rev. Lett. 80, 869–872 (1998).
[Crossref]

P. van Loock and S. L. Braunstein, “Multipartite entanglement for continuous variables: A quantum teleportation network,” Phys. Rev. Lett. 84, 3482–3485 (2000).
[Crossref] [PubMed]

T. Aoki, N. Takei, H. Yonezawa, K. Wakui, T. Hiraoka, and A. Furusawa, “Experimental creation of a fully inseparable tripartite continuous-variable state,” Phys. Rev. Lett. 91, 080404 (2003).
[Crossref] [PubMed]

A. M. Lance, T. Symul, W. P. Bowen, B. C. Sanders, and P. K. Lam, “Tripartite quantum state sharing,” Phys. Rev. Lett. 92, 177903 (2004).
[Crossref] [PubMed]

D. Bouwmeester, J. W. Pan, M. Daniell, H. Weinfurter, and A. Zeilinger, “Observation of three-photon Greenburger-Horne-Zeilinger entanglement,” Phys. Rev. Lett. 82, 1345–1349 (1999).
[Crossref]

J. W. Pan, M. Daniell, S. Gasparoni, G. Weihs, and A. Zeilinger, “Experimental demonstration of four-photon entanglement and high-fidelity teleportation,” Phys. Rev. Lett. 86, 4435–4438 (2001).
[Crossref] [PubMed]

N. Kiesel, C. Schmid, U. Weber, G. Toth, O. Guhne, R. Ursin, and H. Weinfurter, “Experimental analysis of a four-qubit photon cluster state,” Phys. Rev. Lett. 95, 210502 (2005).
[Crossref] [PubMed]

X. Li, Q. Pan, J. Jing, J. Zhang, C. Xie, and K. Peng, “Quantum dense coding exploiting a bright Einstein-Podolsky-Rosen beam,” Phys. Rev. Lett. 88, 047904 (2002).
[Crossref] [PubMed]

C. H. Bennett and S. J. Wiesner, “Communication via one- and two-particle operators on Einstein-Podolsky-Rosen states,” Phys. Rev. Lett. 69, 2881–2884 (1992).
[Crossref] [PubMed]

K. Mattle, H. Weinfurter, P. G. Kwiat, and A. Zeilinger, “Dense coding in experimental quantum communications,” Phys. Rev. Lett. 76, 4656–4659 (1996).
[Crossref] [PubMed]

J. Jing, J. Zhang, Y. Fan, F. Zhao, C. Xie, and K. Peng, “Experimental demonstration of tripartite entanglement and controlled dense coding for continuous variables,” Phys. Rev. Lett. 90, 167903 (2003).
[Crossref] [PubMed]

A. K. Ekert, “Quantum cryptography based on Bell’s theorem,” Phys. Rev. Lett. 67, 661–663 (1991).
[Crossref] [PubMed]

T. Jennewein, C. Simon, G. Weihs, H. Weinfurter, and A. Zeilinger, “Quantum cryptography with entangled photons,” Phys. Rev. Lett. 84, 4729–4732 (2000).
[Crossref] [PubMed]

D. S. Naik, C. G. Peterson, A. G. White, A. J. Berglund, and P. G. Kwiat, “Entangled state quantum cryptography: Eavesdropping on the Ekert protocol,” Phys. Rev. Lett. 84, 4733–4736 (2000).
[Crossref] [PubMed]

W. Tittel, J. Brendel, H. Zbinden, and N. Gisin, “Quantum cryptography using entangled photons in energy-time Bell states,” Phys. Rev. Lett. 84, 4737–4740 (2000).
[Crossref] [PubMed]

R. Raussendorf and H. J. Briegel, “A one-way quantum computer,” Phys. Rev. Lett. 86, 5188–5191 (2001).
[Crossref] [PubMed]

M. A. Nielsen, “Optical quantum computing using cluster states,” Phys. Rev. Lett. 93, 040503 (2004).
[Crossref] [PubMed]

N. C. Menicucci, P. van Loock, M. Gu, C. Weedbrook, T. C. Ralph, and M. A. Nielsen, “Universal quantum computation with continuous-variable cluster states,” Phys. Rev. Lett. 97, 110501 (2006).
[Crossref] [PubMed]

C. H. Bennett, G. Brassard, C. Crepeau, R. Josza, A. Peres, and W. K. Wootters, “Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels,” Phys. Rev. Lett. 70, 1895–1899 (1993).
[Crossref] [PubMed]

Proc. IRE (2)

J.M Manley and H. E. Rowe, “Some general properties of nonlinear elements—Part I. General energy relations,” Proc. IRE 44, 904–913 (1956).
[Crossref]

M. T. Weiss, “Quantum derivation of energy relations analogous to those for nonlinear rectances,” Proc. IRE 45, 1012–1013 (1957).

Science (1)

A. Furusawa, J. L. Sorensen, S. J. Braunstein, C. A. Fuchs, H. J. Kimble, and E. S. Polzik, “Unconditional quantum teleportation,” Science 282, 706–709 (1998).
[Crossref] [PubMed]

Other (5)

J. S. Bell, Speakable and Unspeakable in Quantum Mechanics, 2nd Ed. (Cambridge University Press, 2004).
[Crossref]

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

S. L. Braunstein and A. K. Pati, Quantum Information with Continuous Variables (Kluwer Academic Press, 2003).

S. M. Barnett and P. M. Radmore, Methods in Theoretical Quantum Optics (Oxford University Press, 1997).

R. Loudon, The Quantum Theory of Light, 3rd Ed. (Oxford University Press, 2000).

Cited By

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

Alert me when this article is cited.


Figures (8)

Fig. 1.
Fig. 1.

Frequency diagram for the interaction of two pumps (1 and 2) and four sidebands (1± and 2±). Depending on the fiber dispersion and pump frequencies, six different four-wave mixing (FWM) processes can occur, separately or simultaneously. The red, blue and green dashed lines denote modulation interaction (MI), phase conjugation (PC) and Bragg scattering (BS), respectively.

Fig. 2.
Fig. 2.

Polarization diagram for the four-sideband interaction driven by perpendicular pumps. (a) Special case in which the pump-pump frequency difference is twice the pump-sideband difference. (b) General case in which the pump-pump difference is (much) larger than the pump-sideband difference.

Fig. 3.
Fig. 3.

Quadrature variances and correlations, normalized to the input variance 1/2 and measured in dB, plotted as functions of distance. (a) MI of pump 1, which involves modes 1- and 1+. The solid curve denotes the variance of either mode, whereas the dashed curve denotes the correlation between the modes [Eqs. (23) and (24)]. The local-oscillator phase θ=π/2 and the distance parameter is γKP1z. Similar results apply to the interaction between the superposition modes b + and c +, for which the distance parameter is γK (P 1+P 2)z [Eqs. (37)–(39)]. (b) Four-mode interaction driven by pumps with equal powers. The solid curve denotes the variance of any mode, whereas the dashed curve denotes the correlation between any pair of modes [Eqs. (25)–(32)]. The phase is π/2 and the distance parameter is γKPz.

Fig. 4.
Fig. 4.

(a) Probability (in dB) that there are n photons in each of modes b+ and c+ [Eq. (62)]. The dashed, dot-dashed and solid lines represent the distance parameters γK (P 1+P 2)z=0.3, 1.0 and 3.0, respectively. (b) Joint probability distribution (PD) of modes b+ and c+ [Eq. (63)] for the intermediate distance. These modes are correlated.

Fig. 5.
Fig. 5.

Total probability (in dB) that there are n photons in mode 1-[Eq. (67)]. The dashed, dot-dashed and solid lines represent the distance parameters 2γKPz=0.3, 1.0 and 3.0, respectively. The PDs of modes 1+, 2- and 2+ are identical.

Fig. 6.
Fig. 6.

(a) Joint PD (in dB) of modes 1- and 1+ [Eq. (69)] for the n=4 state and the intermediate distance-parameter 2γKPz=1.0. The joint PD of modes 1- and 2+ is identical. (b) Joint PD of modes 1- and 2- [Eq. (70)] for the same state and distance. These modes are anti-correlated.

Fig. 7.
Fig. 7.

(a) Joint PD (in dB) of modes 1- and 1+ [Eq. (71)] for the intermediate distance-parameter 2γKPz=1.0, which should be compared to the PD shown in Fig. 4(b). The joint PD of modes 1- and 2+ is identical. (b) Joint PD of modes 1- and 2- [Eq. (72)] for the same distance.

Fig. 8.
Fig. 8.

Entanglement (entropy) of mode 1- plotted as a function of the distance parameter 2γKPz. The dashed and solid curves denote the two-mode interaction with mode 1+ [Eq. (73)] and the four-mode interaction with 1+, 2- and 2+ [Eq. (74)], respectively. For comparison, the dot-dashed curve denotes the entropy of mode b +, which interacts with mode c + [also Eq. (73)].

Equations (121)

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

H a = α ( a 1 a 1 + a 1 + a 1 + ) + α ( a 1 a 1 + + a 1 a 1 + )
  + β ( a 1 a 2 + a 1 a 2 ) + β ( a 1 + a 2 + + a 1 + a 2 + )
+ β ( a 1 a 2 + + a 1 a 2 + ) + β ( a 1 + a 2 + a 1 + a 2 )
+ γ ( a 2 a 2 + a 2 + a 2 + ) + γ ( a 2 a 2 + + a 2 a 2 + ) ,
da j dz = i [ a j , H a ]
da 1 dz = i α a 1 i α a 1 + i β a 2 i β a 2 + ,
da 1 + dz = i α a 1 + i α a 1 + + i β a 2 + i β a 2 + ,
da 2 dz = i β a 1 i β a 1 + i γ a 2 i γ a 2 + ,
da 2 + dz = i β a 1 + i β a 1 + + i γ a 2 + i γ a 2 + .
a 1 ( z ) = ( 1 i α z ) a 1 ( 0 ) i α za 1 + ( 0 ) i β za 2 ( 0 ) i β za 2 + ( 0 ) ,
a 1 + ( z ) = i α za 1 ( 0 ) + ( 1 + i α z ) a 1 + ( 0 ) + i β za 2 ( 0 ) + i β za 2 + ( 0 ) ,
a 2 ( z ) = i β za 1 ( 0 ) i β za 1 + ( 0 ) + ( 1 i γ z ) a 2 ( 0 ) i γ za 2 + ( 0 ) ,
a 2 + ( z ) = i β za 1 ( 0 ) + i β za 1 + ( 0 ) + i γ za 2 ( 0 ) + ( 1 + i γ z ) a 2 + ( 0 ) ,
q j ( θ j ) = ( a j e i θ j + a j e i θ j ) 2 1 2 ,
δ q j ( θ j ) = q j ( θ j ) q j ( θ j ) ,
a j ( z ) = k [ μ j k ( z ) a k ( 0 ) + ν j k ( z ) a k ( 0 ) ] .
δ q j ( θ j ) δ q k ( θ k ) = l ( μ j l e i θ j + ν j l * e i θ j ) ( μ kl * e i θ k + ν k l e i θ k ) 2 .
δ q 1 ± 2 ( θ 1 ± ) = [ 1 + 2 ( α 2 + β 2 ) z 2 ] 2 ,
δ q 2 ± 2 ( θ 2 ± ) = [ 1 + 2 ( β 2 + γ 2 ) z 2 ] 2
δ q 1 ( θ 1 ) δ q 1 + ( θ 1 + ) = α z sin ( θ 1 + θ 1 + ) ( α 2 + β 2 ) z 2 cos ( θ 1 + θ 1 + ) ,
δ q 1 ( θ 1 ) δ q 2 ( θ 2 ) = β ( α + γ ) z 2 cos ( θ 1 θ 2 ) ,
δ q 1 ( θ 1 ) δ q 2 + ( θ 2 + ) = β z sin ( θ 1 + θ 2 + ) β ( α + γ ) z 2 cos ( θ 1 + θ 2 + ) ,
δ q 1 + ( θ 1 + ) δ q 2 ( θ 2 ) = β z sin ( θ 1 + + θ 2 ) β ( α + γ ) z 2 cos ( θ 1 + + θ 2 ) ,
δ q 1 + ( θ 1 + ) δ q 2 + ( θ 2 + ) = β ( α + γ ) z 2 cos ( θ 1 + θ 2 + ) ,
δ q 2 ( θ 2 ) δ q 2 + ( θ 2 + ) = γz sin ( θ 2 + θ 2 + ) ( β 2 + γ 2 ) z 2 cos ( θ 2 + θ 2 + ) .
δ q 1 ± 2 ( θ ) [ 1 + 2 ( α z ) 2 ] 2 ,
δ q 1 ( θ ) δ q 1 + ( θ ) ( α z ) sin ( 2 θ ) ( α z ) 2 cos ( 2 θ ) .
δ q 1 ± 2 ( θ ) = [ 1 + 4 ( z ) 2 ] 2 ,
δ q 2 ± 2 ( θ ) = [ 1 + 4 ( z ) 2 ] 2 ,
δ q 1 ( θ ) δ q 1 + ( θ ) = z sin ( 2 θ ) 2 ( z ) 2 cos ( 2 θ ) ,
δ q 1 ( θ ) δ q 2 ( θ ) = 2 ( z ) 2 ,
δ q 1 ( θ ) δ q 2 + ( θ ) = z sin ( 2 θ ) 2 ( z ) 2 cos ( 2 θ ) ,
δ q 1 + ( θ ) δ q 2 ( θ ) = z sin ( 2 θ ) 2 ( z ) 2 cos ( 2 θ ) ,
δ q 1 + ( θ ) δ q 2 + ( θ ) = 2 ( z ) 2 ,
δ q 2 ( θ ) δ q 2 + ( θ ) = z sin ( 2 θ ) 2 ( z ) 2 cos ( 2 θ ) .
b ± = ( a 1 ± a 2 ) 2 1 2 ,
c ± = ( a 1 + ± a 2 + ) 2 1 2 ,
2 δ q b + δ q c ± = δ q 1 δ q 1 + ± δ q 1 δ q 2 + + δ q 2 δ q 1 + ± δ q 2 δ q 2 + ,
2 δ q b δ q c ± = δ q 1 δ q 1 + ± δ q 1 δ q 2 + δ q 2 δ q 1 + δ q 2 δ q 2 + .
δ q b + 2 ( θ ) = [ 1 + 2 ( 2 z ) 2 ] 2 ,
δ q c + 2 ( θ ) = [ 1 + 2 ( 2 z ) 2 ] 2 ,
δ q b + δ q c + ( θ ) = ( 2 z ) sin ( 2 θ ) ( 2 z ) 2 cos ( 2 θ ) .
δ q b 2 ( θ ) = 1 2 ,
δ q c 2 ( θ ) = 1 2 ,
δ q b ( θ ) δ q c ( θ ) = 0 .
b + = ε ( σ a 1 + a 2 ) , b = ε ( a 1 σ a 2 ) ,
c + = ε ( σ a 1 + + a 2 + ) , c = ε ( a 1 + σ a 2 + ) ,
b + ( z ) = [ 1 + i ( σ + 1 σ ) z ] b + ( 0 ) + i ( σ + 1 σ ) z c + ( 0 ) ,
c + ( z ) = i ( σ + 1 σ ) z b + ( 0 ) + [ 1 i ( σ + 1 σ ) z ] c + ( 0 ) .
b ( z ) = b ( 0 ) ,
c ( z ) = c ( 0 ) .
db + dz = ib + + ic + ,
dc + dz = ib + ic + ,
r = ( b + + c + ) 2 1 2 ,
s = ( b + c + ) 2 1 2
dr d z = ir + i r ,
ds d z = is i s ,
r ( z ) = ( 1 + i z ) r ( 0 ) + i z r ( 0 ) ,
s ( z ) = ( 1 + i z ) s ( 0 ) i z s ( 0 ) .
H bc = ( σ + 1 σ ) ( b + b + + c + c + + b + c + + b + c + ) .
H rs = r r + [ ( r ) 2 + r 2 ] 2 + s s [ ( s ) 2 + s 2 ] 2 .
exp ( i H r z ) = exp ( γ + K + ) exp ( γ 3 K 3 ) exp ( γ K ) ,
r = 1 ( 1 iz ) 1 2 n = 0 ( iz 1 iz ) n [ ( 2 n ) ! ] 1 2 2 n n ! 2 n ,
b + , c + = 1 1 i z n = 0 ( i z 1 i z ) n n , n ,
A ( n , z ) = z 2 n ( 1 + z 2 ) n + 1 .
Q ( k , l , z ) = A ( k , z ) δ ( k , l ) ,
ψ ( z ) = 1 1 i z n = 0 k = 0 n l = 0 n ( i z 1 i z ) n σ k + l n ! k , l , n k , n l ( 1 + σ 2 ) n [ k ! l ! ( n k ) ! ( n l ) ! ] 1 2 ,
ψ ( z ) 1 1 i z n = 0 ( i z 1 i z ) n n , n , 0 , 0 ,
ψ ( z ) 1 1 i z n = 0 k = 0 n l = 0 n ( i z 1 i z ) n n ! k , l , n k , n l 2 n [ k ! l ! ( n k ) ! ( n l ) ! ] 1 2 .
P t ( m , z ) = n = m A ( n , z ) B ( n , m , n m ) ,
B ( n , k , l ) = n ! ( 2 n k ! l ! ) .
Q c ( k , l ) = B ( n , k , n k ) B ( n , l , n l ) .
R c ( k , l ) = B ( n , k , n k ) δ ( n k , l ) .
Q t ( k , l , z ) = n = max ( k , l ) A ( n , z ) B ( n , k , n k ) B ( n , l , n l ) .
R t ( k , l , z ) = A ( k + l , z ) B ( k + l , k , l ) .
ρ b + ( z ) = n = 0 A n z n n ,
ρ 1 ( z ) = m = 0 P t m z m m ,
d z n 1 = i α ( a 1 a 1 + a 1 a 1 + ) + i β ( a 1 a 2 a 1 a 2 )
+ i β ( a 1 a 2 + a 1 a 2 + ) ,
d z n 1 + = i α ( a 1 a 1 + a 1 a 1 + ) + i β ( a 1 + a 2 a 1 + a 2 )
+ i β ( a 1 + a 2 + a 1 + a 2 + ) ,
d z n 2 = ( a 2 a 2 + a 2 a 1 + ) + i β ( a 1 a 2 a 1 a 2 )
+ i β ( a 1 + a 2 a 1 + a 2 ) ,
d z n 2 + = ( a 2 a 2 + a 2 a 2 + ) + i β ( a 1 a 2 + a 1 a 2 + )
            + i β ( a 1 + a 2 + a 1 + a 2 + ) .
d z ( n 1 n 1 + ) = d z ( n 2 + n 2 ) ,
d z ( n 1 + n 2 ) = d z ( n 1 + + n 2 + ) ,
d z ( n 1 n 2 + ) = d z ( n 1 + n 2 ) .
exp ( a ) b exp ( a ) = n = 0 [ a , b ] n n ! , ,
exp ( a ) b exp ( a ) = n = 0 m = 0 n a m b ( a ) n m m ! ( n n ) ! .
[ a , b ] n = m = 0 n n ! a m b ( a ) n m m ! ( n m ) ! .
a [ a , b ] n [ a , b ] n a = m = 0 n n ! [ a m + 1 b ( a ) n m a m b ( a ) n m a ] m ! ( n m ) ! ,
= m = 1 n + 1 n ! a m b ( a ) n + 1 m ( m 1 ) ! ( n + 1 m ) ! + m = 0 n n ! a m b ( a ) n + 1 m m ! ( n m ) ! .
n ! a m b ( a ) n + 1 m ( m 1 ) ! ( n m ) ! [ 1 n + 1 m + 1 m ] = ( n + 1 ) ! a m b ( a ) n + 1 m m ! ( n + 1 m ) ! .
F ( z ) = exp [ i ( K + + 2 K 3 + K ) z ] .
F ( z ) = exp [ ip ( z ) K + ] exp [ iq ( z ) K 3 ] exp [ ir ( z ) K ] ,
F = i ( K + + 2 K 3 + K ) F ,
F = ( i p K + + I q e i p K + K 3 e i p K + + i r e i p K + e i q K 3 K e i q K 3 e i p K + ) F .
e i p K + K 3 e i p K + = K 3 i p K + ,
e i q K 3 K e i q K 3 = K e i q ,
e i p K + K e i p K + = K 2 i p K 3 p 2 K + .
p i p q p 2 ( r e i q ) = 1 ,
q 2 i p ( r e i q ) = 2 ,
r e i q = 1 ,
i p ( z ) = i z ( 1 i z ) ,
i q ( z ) = 2 log ( 1 i z ) ,
i r ( z ) = i z ( 1 i z ) .
ψ = n = 0 a n n b n c ,
ρ = n = 0 n = 0 a n a n * n b n c n b n c .
ρ b = n = 0 a n 2 n b n b .
ψ = n = 0 k = 0 n l = 0 n a n b nk b nl k 1 l 2 n k 3 n l 4 ,
ρ = n = 0 k = 0 n l = 0 n n = 0 k = 0 n l = 0 n a n b nk b nl ( a n b n k b n l ) *
× k 1 l 2 n k 3 n l 4 k 1 l 2 n k 3 n l 4 .
ρ 234 = k = 0 n = k l = 0 n n = k l = 0 n a n b nk b nl ( a n b n k b n l ) *
× l 2 n k 3 n l 4 l 2 n k 3 n l 4 .
ρ 24 = n = 0 k = 0 n l = 0 n l = 0 n a n 2 b nk 2 b nl b nl * l 2 n l 4 l 2 n l 4 .
ρ 24 = n = 0 l = 0 n l = 0 n a n 2 b nl b nl * l 2 n - l 4 l 2 n - l 4 .
ρ 4 = l = 0 n = l a n 2 b nl 2 n l 4 n l 4 ,
ρ 4 = l = 0 n = l a n 2 b nl 2 l 4 l 4 ,
ρ 34 = l = 0 n = l n = l k = 0 k + ( a n b nk b nl ) ( a n b n k b n l ) * n k 3 n l 4 n k 3 n l 4 .
ρ 4 = n = 0 l = 0 n k = 0 n a n 2 b nk 2 b nl 2 n l 4 n l 4 .

Metrics