Abstract

We propose a protocol sharing Einstein–Podolsky–Rosen pairs based on weak cross-Kerr nonlinearities and the coherent state at first. If the security check is passed, the checked photons can be applied in the next communication process due to the application of quantum nondemolition measurements, which improves the efficiency and the security of the distribution process. As its applications, we present two quantum key distribution protocols. A random key can be transmitted using the path analyzers based on the idea of BBM92-QKD protocol. Moreover, the sender performs the parity measurement and publicizes the measurement outcomes, and thus the recipient performs computational basis measurements to obtain a deterministic key.

© 2012 Optical Society of America

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  1. C. H. Bennett and G. Brassard, “Quantum cryptography: public key distribution and coin tossing,” in Proceedings of IEEE International Conference on Computer, Systems and Signal Processing (IEEE, 1984), pp. 175–179.
  2. C. H. Bennett, “Quantum cryptography using any two nonorthogonal states,” Phys. Rev. Lett. 68, 3121–3124 (1992).
    [CrossRef]
  3. A. K. Ekert, “Quantum cryptography based on Bells theorem,” Phys. Rev. Lett. 67, 661–663 (1991).
    [CrossRef]
  4. J. S. Bell, “On the Einstein Podolsky Rosen paradox,” Physics 1, 195–200 (1964).
  5. J. Clauser, M. Horne, A. Shimony, and R. Holt, “Proposed experiment to test local hidden-variable theories,” Phys. Rev. Lett. 23, 880–884 (1969).
    [CrossRef]
  6. C. Bennett, G. Brassard, and N. Mermin, “Quantum cryptography without Bells theorem,” Phys. Rev. Lett. 68, 557–559 (1992).
    [CrossRef]
  7. D. Dieks, “Communication by EPR devices,” Phys. Lett. A 92, 271–272 (1982).
    [CrossRef]
  8. W. K. Wootters and W. H. Zurek, “A single quantum cannot be cloned,” Nature 299, 802–803 (1982).
    [CrossRef]
  9. D. Bruß, “Optimal eavesdropping in quantum cryptography with six states,” Phys. Rev. Lett. 81, 3018–3021 (1998).
    [CrossRef]
  10. P. Xue, C.-F. Li, and G.-C. Guo, “Conditional efficient multiuser quantum cryptography network,” Phys. Rev. A 65, 022317 (2002).
    [CrossRef]
  11. G. L. Long and X. S. Liu, “Theoretically efficient high-capacity quantum-key-distribution scheme,” Phys. Rev. A 65, 032302 (2002).
    [CrossRef]
  12. F.-G. Deng and G. L. Long, “Controlled order rearrangement encryption for quantum key distribution,” Phys. Rev. A 68, 042315 (2003).
    [CrossRef]
  13. F.-G. Deng and G. L. Long, “Bidirectional quantum key distribution protocol with practical faint laser pulses,” Phys. Rev. A 70, 012311 (2004).
    [CrossRef]
  14. K. Tamaki, “Quantum circuit for the proof of the security of quantum key distribution without encryption of error syndrome and noisy processing,” Phys. Rev. A 81, 022316 (2010).
    [CrossRef]
  15. A. R. Dixon, Z. L. Yuan, J. F. Dynes, A. W. Sharpe, and A. J. Shields, “Continuous operation of high bit rate quantum key distribution,” Appl. Phys. Lett. 96, 161102 (2010).
    [CrossRef]
  16. S. J. Phoenix, S. M. Barnett, P. D. Townsend, and K. Blow, “Multi-user quantum cryptography on optical networks,” J. Mod. Opt. 42, 1155–1163 (1995).
    [CrossRef]
  17. D. Elkouss, J. Martinez-Mateo, and V. Martin, “Information reconciliation for quantum key distribution,” Quantum Inf. Comput. 11, 0226–0238 (2011).
  18. N. Lütkenhaus, J. Calsamiglia, and K.-A. Suominen, “Bell measurements for teleportation,” Phys. Rev. A 59, 3295–3300 (1999).
    [CrossRef]
  19. D. Bouwmeester, “Bit-flip-error rejection in optical quantum communication,” Phys. Rev. A 63, 040301(R) (2001).
    [CrossRef]
  20. D. Kalamidas, “Feasible quantum error detection with linear optics,” Phys. Lett. A 321, 87–93 (2004).
    [CrossRef]
  21. X.-B. Wang, “Fault tolerant quantum key distribution protocol with collective random unitary noise,” Phys. Rev. A 72, 050304(R) (2005).
  22. C. Wang, Y. Zhang, and G.-S. Jin, “Entanglement purification and concentration of electron-spin entangled states using quantum-dot spins in optical microcavities,” Phys. Rev. A 84, 032307 (2011).
    [CrossRef]
  23. F.-G. Deng, “Efficient multipartite entanglement purification with the entanglement link from a subspace,” Phys. Rev. A 84, 052312 (2011).
    [CrossRef]
  24. 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]
  25. S. D. Barrett and G. J. Milburn, “Quantum-information processing via a lossy bus,” Phys. Rev. A 74, 060302(R) (2006).
    [CrossRef]
  26. T. P. Spiller, K. Nemoto, S. L. Braunstein, W. J. Munro, P. V. Loock, and G. J. Milburn, “Quantum computation by communication,” New J. Phys. 8, 30 (2006).
    [CrossRef]
  27. S. G. R. Louis, K. Nemoto, W. J. Munro, and T. P. Spiller, “The efficiencies of generating cluster states with weak nonlinearities,” New J. Phys. 9, 193 (2007).
    [CrossRef]
  28. S. Louis, K. Nemoto, W. Munro, and T. Spiller, “Weak nonlinearities and cluster states,” Phys. Rev. A 75, 042323 (2007).
    [CrossRef]
  29. C. C. Gerry and T. Bui, “Quantum non-demolition measurement of photon number using weak nonlinearities,” Phys. Lett. A 372, 7101–7104 (2008).
    [CrossRef]
  30. J. Shapiro, “Single-photon Kerr nonlinearities do not help quantum computation,” Phys. Rev. A 73, 062305 (2006).
    [CrossRef]
  31. J. H. Shapiro and M. Razavi, “Continuous-time cross-phase modulation and quantum computation,” New J. Phys. 9, 16 (2007).
    [CrossRef]
  32. P. Kok, “Effects of self-phase-modulation on weak nonlinear optical quantum gates,” Phys. Rev. A 77, 013808 (2008).
    [CrossRef]
  33. 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]
  34. 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]
  35. G. Milburn and D. Walls, “State reduction in quantum-counting quantum nondemolition measurements,” Phys. Rev. A 30, 56–60 (1984).
    [CrossRef]
  36. N. Imoto, H. Haus, and Y. Yamamoto, “Quantum nondemolition measurement of the photon number via the optical Kerr effect,” Phys. Rev. A 32, 2287–2292 (1985).
    [CrossRef]
  37. I. L. Chuang and Y. Yamamoto, “Quantum bit regeneration,” Phys. Rev. Lett. 76, 4281–4284 (1996).
    [CrossRef]
  38. P. Grangier, J. A. Levenson, and J.-P. Poizat, “Quantum non-demolition measurements in optics,” Nature 396, 537–542 (1998).
    [CrossRef]
  39. J. C. Howell and J. A. Yeazell, “Nondestructive single-photon trigger,” Phys. Rev. A 62, 032311 (2000).
    [CrossRef]
  40. A. D. Greentree, R. G. Beausoleil, L. C. L. Hollenberg, W. J. Munro, K. Nemoto, S. Prawer, and T. P. Spiller, “Single photon quantum non-demolition measurements in the presence of inhomogeneous broadening,” New J. Phys. 11, 93005 (2009).
    [CrossRef]
  41. 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).
  42. 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]
  43. K. Nemoto and W. J. Munro, “Nearly deterministic linear optical controlled-NOT gate,” Phys. Rev. Lett. 93, 250502 (2004).
    [CrossRef]
  44. Q. Lin and J. Li, “Quantum control gates with weak cross-Kerr nonlinearity,” Phys. Rev. A 79, 22301 (2009).
    [CrossRef]
  45. 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).
  46. 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]
  47. N. B. An, K. Kim, and J. Kim, “Generation of cluster-type entangled coherent states using weak nonlinearities and intense laser beams,” Quantum Inf. Comput. 11, 0124–0141 (2011).
  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.-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]
  51. 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]
  52. L.-L. Sun, H.-F. Wang, S. Zhang, and K.-H. Yeon, “Entanglement concentration of partially entangled three-photon W states with weak cross-Kerr nonlinearity,” J. Opt. Soc. Am. B 29, 630–634 (2012).
    [CrossRef]
  53. Y. Xia, Q.-Q. Chen, J. Song, and H.-S. Song, “Efficient hyperentangled Greenberger–Horne–Zeilinger states analysis with cross-Kerr nonlinearity,” J. Opt. Soc. Am. B 29, 1029–1037 (2012).
    [CrossRef]
  54. F.-F. Du, T. Li, B.-C. Ren, H.-R. Wei, and F.-G. Deng, “Single-photon-assisted entanglement concentration of a multiphoton system in a partially entangled W state with weak cross-Kerr nonlinearity,” J. Opt. Soc. Am. B 29, 1399–1405 (2012).
    [CrossRef]
  55. K. Edamatsu, “Entangled photons: generation, observation, and characterization,” Jpn. J. Appl. Phys. 46, 7175–7187 (2007).
    [CrossRef]
  56. F.-G. Deng, G.-L. Long, and X.-S. Liu, “Two-step quantum direct communication protocol using the Einstein-Podolsky-Rosen pair block,” Phys. Rev. A 68, 042317 (2003).
    [CrossRef]
  57. 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]
  58. M. P. Hedges, J. J. Longdell, Y. Li, and M. J. Sellars, “Efficient quantum memory for light,” Nature 465, 1052–1056 (2010).
    [CrossRef]
  59. C. Clausen, I. Usmani, F. Bussières, N. Sangouard, M. Afzelius, H. de Riedmatten, and N. Gisin, “Quantum storage of photonic entanglement in a crystal,” Nature 469, 508–511 (2011).
    [CrossRef]
  60. 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]
  61. S. Phoenix, “Wave-packet evolution in the damped oscillator,” Phys. Rev. A 41, 5132–5138 (1990).
    [CrossRef]
  62. H. Jeong, “Quantum computation using weak nonlinearities: robustness against decoherence,” Phys. Rev. A 73, 052320 (2006).
    [CrossRef]

2012

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).

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]

L.-L. Sun, H.-F. Wang, S. Zhang, and K.-H. Yeon, “Entanglement concentration of partially entangled three-photon W states with weak cross-Kerr nonlinearity,” J. Opt. Soc. Am. B 29, 630–634 (2012).
[CrossRef]

Y. Xia, Q.-Q. Chen, J. Song, and H.-S. Song, “Efficient hyperentangled Greenberger–Horne–Zeilinger states analysis with cross-Kerr nonlinearity,” J. Opt. Soc. Am. B 29, 1029–1037 (2012).
[CrossRef]

F.-F. Du, T. Li, B.-C. Ren, H.-R. Wei, and F.-G. Deng, “Single-photon-assisted entanglement concentration of a multiphoton system in a partially entangled W state with weak cross-Kerr nonlinearity,” J. Opt. Soc. Am. B 29, 1399–1405 (2012).
[CrossRef]

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]

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]

N. B. An, K. Kim, and J. Kim, “Generation of cluster-type entangled coherent states using weak nonlinearities and intense laser beams,” Quantum Inf. Comput. 11, 0124–0141 (2011).

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, 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]

C. Clausen, I. Usmani, F. Bussières, N. Sangouard, M. Afzelius, H. de Riedmatten, and N. Gisin, “Quantum storage of photonic entanglement in a crystal,” Nature 469, 508–511 (2011).
[CrossRef]

D. Elkouss, J. Martinez-Mateo, and V. Martin, “Information reconciliation for quantum key distribution,” Quantum Inf. Comput. 11, 0226–0238 (2011).

C. Wang, Y. Zhang, and G.-S. Jin, “Entanglement purification and concentration of electron-spin entangled states using quantum-dot spins in optical microcavities,” Phys. Rev. A 84, 032307 (2011).
[CrossRef]

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

2010

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]

K. Tamaki, “Quantum circuit for the proof of the security of quantum key distribution without encryption of error syndrome and noisy processing,” Phys. Rev. A 81, 022316 (2010).
[CrossRef]

A. R. Dixon, Z. L. Yuan, J. F. Dynes, A. W. Sharpe, and A. J. Shields, “Continuous operation of high bit rate quantum key distribution,” Appl. Phys. Lett. 96, 161102 (2010).
[CrossRef]

M. P. Hedges, J. J. Longdell, Y. Li, and M. J. Sellars, “Efficient quantum memory for light,” Nature 465, 1052–1056 (2010).
[CrossRef]

2009

Q. Lin and J. Li, “Quantum control gates with weak cross-Kerr nonlinearity,” Phys. Rev. A 79, 22301 (2009).
[CrossRef]

A. D. Greentree, R. G. Beausoleil, L. C. L. Hollenberg, W. J. Munro, K. Nemoto, S. Prawer, and T. P. Spiller, “Single photon quantum non-demolition measurements in the presence of inhomogeneous broadening,” New J. Phys. 11, 93005 (2009).
[CrossRef]

2008

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]

P. Kok, “Effects of self-phase-modulation on weak nonlinear optical quantum gates,” Phys. Rev. A 77, 013808 (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

S. G. R. Louis, K. Nemoto, W. J. Munro, and T. P. Spiller, “The efficiencies of generating cluster states with weak nonlinearities,” New J. Phys. 9, 193 (2007).
[CrossRef]

S. Louis, K. Nemoto, W. Munro, and T. Spiller, “Weak nonlinearities and cluster states,” Phys. Rev. A 75, 042323 (2007).
[CrossRef]

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

K. Edamatsu, “Entangled photons: generation, observation, and characterization,” Jpn. J. Appl. Phys. 46, 7175–7187 (2007).
[CrossRef]

2006

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

T. P. Spiller, K. Nemoto, S. L. Braunstein, W. J. Munro, P. V. Loock, and G. J. Milburn, “Quantum computation by communication,” New J. Phys. 8, 30 (2006).
[CrossRef]

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]

X.-B. Wang, “Fault tolerant quantum key distribution protocol with collective random unitary noise,” Phys. Rev. A 72, 050304(R) (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).

2004

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

F.-G. Deng and G. L. Long, “Bidirectional quantum key distribution protocol with practical faint laser pulses,” Phys. Rev. A 70, 012311 (2004).
[CrossRef]

D. Kalamidas, “Feasible quantum error detection with linear optics,” Phys. Lett. A 321, 87–93 (2004).
[CrossRef]

2003

F.-G. Deng and G. L. Long, “Controlled order rearrangement encryption for quantum key distribution,” Phys. Rev. A 68, 042315 (2003).
[CrossRef]

F.-G. Deng, G.-L. Long, and X.-S. Liu, “Two-step quantum direct communication protocol using the Einstein-Podolsky-Rosen pair block,” Phys. Rev. A 68, 042317 (2003).
[CrossRef]

2002

P. Xue, C.-F. Li, and G.-C. Guo, “Conditional efficient multiuser quantum cryptography network,” Phys. Rev. A 65, 022317 (2002).
[CrossRef]

G. L. Long and X. S. Liu, “Theoretically efficient high-capacity quantum-key-distribution scheme,” Phys. Rev. A 65, 032302 (2002).
[CrossRef]

2001

D. Bouwmeester, “Bit-flip-error rejection in optical quantum communication,” Phys. Rev. A 63, 040301(R) (2001).
[CrossRef]

2000

J. C. Howell and J. A. Yeazell, “Nondestructive single-photon trigger,” Phys. Rev. A 62, 032311 (2000).
[CrossRef]

1999

N. Lütkenhaus, J. Calsamiglia, and K.-A. Suominen, “Bell measurements for teleportation,” Phys. Rev. A 59, 3295–3300 (1999).
[CrossRef]

1998

D. Bruß, “Optimal eavesdropping in quantum cryptography with six states,” Phys. Rev. Lett. 81, 3018–3021 (1998).
[CrossRef]

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

1996

I. L. Chuang and Y. Yamamoto, “Quantum bit regeneration,” Phys. Rev. Lett. 76, 4281–4284 (1996).
[CrossRef]

1995

S. J. Phoenix, S. M. Barnett, P. D. Townsend, and K. Blow, “Multi-user quantum cryptography on optical networks,” J. Mod. Opt. 42, 1155–1163 (1995).
[CrossRef]

1992

C. H. Bennett, “Quantum cryptography using any two nonorthogonal states,” Phys. Rev. Lett. 68, 3121–3124 (1992).
[CrossRef]

C. Bennett, G. Brassard, and N. Mermin, “Quantum cryptography without Bells theorem,” Phys. Rev. Lett. 68, 557–559 (1992).
[CrossRef]

1991

A. K. Ekert, “Quantum cryptography based on Bells theorem,” Phys. Rev. Lett. 67, 661–663 (1991).
[CrossRef]

1990

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

1985

N. Imoto, H. Haus, and Y. Yamamoto, “Quantum nondemolition measurement of the photon number via the optical Kerr effect,” Phys. Rev. A 32, 2287–2292 (1985).
[CrossRef]

1984

G. Milburn and D. Walls, “State reduction in quantum-counting quantum nondemolition measurements,” Phys. Rev. A 30, 56–60 (1984).
[CrossRef]

1982

D. Dieks, “Communication by EPR devices,” Phys. Lett. A 92, 271–272 (1982).
[CrossRef]

W. K. Wootters and W. H. Zurek, “A single quantum cannot be cloned,” Nature 299, 802–803 (1982).
[CrossRef]

1969

J. Clauser, M. Horne, A. Shimony, and R. Holt, “Proposed experiment to test local hidden-variable theories,” Phys. Rev. Lett. 23, 880–884 (1969).
[CrossRef]

1964

J. S. Bell, “On the Einstein Podolsky Rosen paradox,” Physics 1, 195–200 (1964).

Afzelius, M.

C. Clausen, I. Usmani, F. Bussières, N. Sangouard, M. Afzelius, H. de Riedmatten, and N. Gisin, “Quantum storage of photonic entanglement in a crystal,” Nature 469, 508–511 (2011).
[CrossRef]

An, N. B.

N. B. An, K. Kim, and J. Kim, “Generation of cluster-type entangled coherent states using weak nonlinearities and intense laser beams,” Quantum Inf. Comput. 11, 0124–0141 (2011).

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]

Barnett, S. M.

S. J. Phoenix, S. M. Barnett, P. D. Townsend, and K. Blow, “Multi-user quantum cryptography on optical networks,” J. Mod. Opt. 42, 1155–1163 (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.

A. D. Greentree, R. G. Beausoleil, L. C. L. Hollenberg, W. J. Munro, K. Nemoto, S. Prawer, and T. P. Spiller, “Single photon quantum non-demolition measurements in the presence of inhomogeneous broadening,” New J. Phys. 11, 93005 (2009).
[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).

Bell, J. S.

J. S. Bell, “On the Einstein Podolsky Rosen paradox,” Physics 1, 195–200 (1964).

Bennett, C.

C. Bennett, G. Brassard, and N. Mermin, “Quantum cryptography without Bells theorem,” Phys. Rev. Lett. 68, 557–559 (1992).
[CrossRef]

Bennett, C. H.

C. H. Bennett, “Quantum cryptography using any two nonorthogonal states,” Phys. Rev. Lett. 68, 3121–3124 (1992).
[CrossRef]

C. H. Bennett and G. Brassard, “Quantum cryptography: public key distribution and coin tossing,” in Proceedings of IEEE International Conference on Computer, Systems and Signal Processing (IEEE, 1984), pp. 175–179.

Blow, K.

S. J. Phoenix, S. M. Barnett, P. D. Townsend, and K. Blow, “Multi-user quantum cryptography on optical networks,” J. Mod. Opt. 42, 1155–1163 (1995).
[CrossRef]

Bouwmeester, D.

D. Bouwmeester, “Bit-flip-error rejection in optical quantum communication,” Phys. Rev. A 63, 040301(R) (2001).
[CrossRef]

Brassard, G.

C. Bennett, G. Brassard, and N. Mermin, “Quantum cryptography without Bells theorem,” Phys. Rev. Lett. 68, 557–559 (1992).
[CrossRef]

C. H. Bennett and G. Brassard, “Quantum cryptography: public key distribution and coin tossing,” in Proceedings of IEEE International Conference on Computer, Systems and Signal Processing (IEEE, 1984), pp. 175–179.

Braunstein, S. L.

T. P. Spiller, K. Nemoto, S. L. Braunstein, W. J. Munro, P. V. Loock, and G. J. Milburn, “Quantum computation by communication,” New J. Phys. 8, 30 (2006).
[CrossRef]

Bruß, D.

D. Bruß, “Optimal eavesdropping in quantum cryptography with six states,” Phys. Rev. Lett. 81, 3018–3021 (1998).
[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]

Bussières, F.

C. Clausen, I. Usmani, F. Bussières, N. Sangouard, M. Afzelius, H. de Riedmatten, and N. Gisin, “Quantum storage of photonic entanglement in a crystal,” Nature 469, 508–511 (2011).
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Figures (3)

Fig. 1.
Fig. 1.

Schematic plot for the reverse parity analysis. Alice (left part) and Bob (right part) randomly select photons’ paths by path selection (PS) setup. The photons passing through paths ‘1,’ ‘3’ (‘2,’ ‘4’) are to be analyzed by exploiting the { | H , | V } ( { | + , | } ) basis.

Fig. 2.
Fig. 2.

Schematic plot of the parity analysis in Alice’s site on the encoded photon I i and photon A i .

Fig. 3.
Fig. 3.

Illustration plot for loss check of the signal photons. The parity analyses with the probe coherent states | α (in red line) and | α (in blue line) are performed.

Equations (9)

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

| Ψ A i , B i = 1 2 ( | H V | V H ) A i , B i = 1 2 ( | + | + ) A i , B i ,
| Ψ ( 0 ) = 1 2 ( | H V A , B | α p | V H A , B | α e i θ p ) .
ρ t = J ^ ρ + L ^ ρ , J ^ ρ = γ a ρ a , L ^ ρ = γ 2 ( a a ρ + ρ a a ) ,
ρ ( t ) = D ˜ ( t ) ρ ( 0 ) ,
D ˜ ( t ) = exp [ ( J ^ + L ^ ) t ] = exp L ^ t exp [ J ^ γ ( 1 e γ t ) ] .
D ˜ ( t ) ( | α β | ) = exp { ( 1 e γ t ) [ 1 2 ( | α | 2 + | β | 2 ) α β * ] } | A α A β | ,
ρ ( t ) = D ˜ ( t ) | Ψ ( 0 ) Ψ ( 0 ) | = 1 2 ( | H V H V | | A α A α | + | V H V H | | A α e i θ A α e i θ | C | H V V H | | A α A α e i θ | C * | V H H V | | A α e i θ A α | )
ρ ( t ) = 1 2 ( | H V H V | + | V H V H | C | H V V H | C * | V H H V | ) | A α A α | .
p err = 1 2 ( 1 Re ( C ) ) = 1 2 [ 1 e α 2 ( 1 cos θ ) ( 1 e γ t ) ] .

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