Abstract

We propose a scheme to accomplish the optimal symmetric quantum cloning machine using a weak cross-Kerr nonlinearity effect without ancillary photons. Normal coherence probe beam and highly efficient homodyne detection are used to construct this near-deterministic equipment. Feed-forward and feed-backward processes are used to improve the efficiency of success. This device can be used for deterministic implementation of both northern and southern hemispheres optimal cloning transformation by adjusting some devices of the quantum circuit conveniently. The actual feasibility of this scheme with current experiment technology in theory is also discussed.

© 2012 Optical Society of America

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  2. G. L. Long and X. S. Liu, “Theoretically efficient high-capacity quantum-key-distribution scheme,” Phys. Rev. A 65, 032302 (2002).
    [CrossRef]
  3. N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, “Quantum cryptography,” Rev. Mod. Phys. 74, 145–195 (2002).
    [CrossRef]
  4. F. G. Deng and G. L. Long, “Controlled order rearrangement encryption for quantum key distribution,” Phys. Rev. A 68, 042315 (2003).
    [CrossRef]
  5. F. G. Deng and G. L. Long, “Secure direct communication with a quantum one-time-pad,” Phys. Rev. A 69, 052319 (2004).
    [CrossRef]
  6. F. G. Deng and G. L. Long, “Bidirectional quantum key distribution protocol with practical faint laser pulses,” Phys. Rev. A 70, 012311 (2004).
    [CrossRef]
  7. X. H. Li, F. G. Deng, and H. Y. Zhou, “Efficient quantum key distribution over a collective noise channel,” Phys. Rev. A 78, 022321 (2008).
    [CrossRef]
  8. W. K. Wootters and W. H. Zurek, “A single quantum cannot be cloned,” Nature 299, 802–803 (1982).
    [CrossRef]
  9. D. Dieks, “Communication by EPR devices,” Phys. Lett. A 92, 271–272 (1982).
    [CrossRef]
  10. L. M. Duan and G. C. Guo, “Probabilistic cloning and identification of linearly independent quantum states,” Phys. Rev. Lett. 80, 4999–5002 (1998).
    [CrossRef]
  11. V. Bužek and M. Hillery, “Quantum copying: beyond the no-cloning theorem,” Phys. Rev. A 54, 1844–1852 (1996).
    [CrossRef]
  12. R. F. Werner, “Optimal cloning of pure states,” Phys. Rev. A 58, 1827–1832 (1998).
    [CrossRef]
  13. J. Fiurášek, R. Filip, and N. J. Cerf, “Highly asymmetric quantum cloning in arbitrary dimension,” Quantum Inf. Comput. 5, 583–592 (2005).
  14. J. Fiurášek and N. J. Cerf, “Quantum cloning of a pair of orthogonally polarized photons with linear optics,” Phys. Rev. A 77, 052308 (2008).
    [CrossRef]
  15. J. Fiurášek, “Optical implementation of continuous-variable quantum cloning machines,” Phys. Rev. Lett. 86, 4942–4945 (2001).
    [CrossRef]
  16. H. K. Cummins, C. Jones, A. Furze, N. F. Soffe, M. Mosca, J. M. Peach, and J. A. Jones, “Approximate quantum cloning with nuclear magnetic resonance,” Phys. Rev. Lett. 88, 187901 (2002).
    [CrossRef]
  17. A. L. Linares, C. Simon, J. C. Howell, and D. Bouwmeester, “Experimental quantum cloning of single photons,” Science 296, 712–714 (2002).
    [CrossRef]
  18. M. Sabuncu, G. Leuchs, and U. L. Andersen, “Experimental continuous-variable cloning of partial quantum information,” Phys. Rev. A 78, 052312 (2008).
    [CrossRef]
  19. Y. N. Wang, H. D. Shi, L. Jing, X. J. Ren, L. Z. Mu, and H. Fan, “Unified universal quantum cloning machine and fidelities,” Phys. Rev. A 84, 034302 (2011).
    [CrossRef]
  20. D. Bruss, M. Cinchetti, G. M. D’Ariano, and C. Macchiavello, “Phase-covariant quantum cloning,” Phys. Rev. A 62, 012302 (2000).
    [CrossRef]
  21. H. Fan, K. Matsumoto, X. B. Wang, and M. Wadati, “Quantum cloning machines for equatorial qubits,” Phys. Rev. A 65, 012304 (2001).
    [CrossRef]
  22. J. Fiurášek, “Optical implementations of the optimal phase-covariant quantum cloning machine,” Phys. Rev. A 67, 052314 (2003).
    [CrossRef]
  23. X. Y. Pan, G. Q. Liu, L. L. Yang, and H. Fan, “Solid-state optimal phase-covariant quantum cloning machine,” Appl. Phys. Lett. 99, 051113 (2011).
    [CrossRef]
  24. J. F. Du, T. Durt, P. Zou, H. Li, L. C. Kwek, C. H. Lai, C. H. Oh, and A. Ekert, “Experimental quantum cloning with prior partial information,” Phys. Rev. Lett. 94, 040505 (2005).
    [CrossRef]
  25. H. W. Chen, X. Y. Zhou, D. Suter, and J. F. Du, “Experimental realization of 1→2 asymmetric phase-covariant quantum cloning,” Phys. Rev. A 75, 012317 (2007).
    [CrossRef]
  26. C. H. Bennett and G. Brassard, “Quantum cryptography: public-key distribution and coin tossing,” in Proceedings of the IEEE International Conference on Computers, Systems, and Signal Processing, Bangalore, India, (IEEE, 1984), pp. 175–179.
  27. A. K. Ekert, “Quantum cryptography based on Bells theorem,” Phys. Rev. Lett. 67, 661–663 (1991).
    [CrossRef]
  28. C. H. Bennett, “Quantum cryptography using any two nonorthogonal states,” Phys. Rev. Lett. 68, 3121–3124 (1992).
    [CrossRef]
  29. F. Agnes and L. Norbert, “Symmetries in quantum key distribution and the connection between optimal attacks and optimal cloning,” Phys. Rev. A 85, 052310 (2012).
    [CrossRef]
  30. K. Nemoto and W. J. Munro, “Nearly deterministic linear optical controlled-NOT gate,” Phys. Rev. Lett. 93, 250502 (2004).
    [CrossRef]
  31. Q. Lin and J. Li, “Quantum control gates with weak cross-Kerr nonlinearity,” Phys. Rev. A 79, 022301 (2009).
    [CrossRef]
  32. 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).
  33. X. G. Song, X. L. Feng, L. C. Kwek, and C. H. Oh, “Entanglement purification based on photonic polarization parity measurements,” J. Phys. B. At. Mol. Opt. Phys. 38, 2827–2832 (2005).
    [CrossRef]
  34. Y. B. Sheng, F. G. Deng, and H. Y. Zhou, “Efficient polarization-entanglement purification based on parametric down-conversion sources with cross-Kerr nonlinearity,” Phys. Rev. A 77, 042308 (2008).
    [CrossRef]
  35. Y. B. Sheng, F. G. Deng, B. K. Zhao, T. J. Wang, and H. Y. Zhou, “Multipartite entanglement purification with quantum nondemolition detectors,” Eur. Phys. J. D 55, 235–242 (2009).
    [CrossRef]
  36. Y. B. Sheng and F. G. Deng, “Deterministic entanglement purification and complete nonlocal Bell-state analysis with hyperentanglement,” Phys. Rev. A 81, 032307 (2010).
    [CrossRef]
  37. F. G. Deng, “Efficient multipartite entanglement purification with the entanglement link from a subspace,” Phys. Rev. A 84, 052312 (2011).
    [CrossRef]
  38. Y. B. Sheng, F. G. Deng, and H. Y. Zhou, “Nonlocal entanglement concentration scheme for partially entangled multipartite systems with nonlinear optics,” Phys. Rev. A 77, 062325(2008).
    [CrossRef]
  39. F. G. Deng, “Optimal nonlocal multipartite entanglement concentration based on projection measurements,” Phys. Rev. A 85, 022311 (2012).
    [CrossRef]
  40. Y. B. Sheng, F. G. Deng, and H. Y. Zhou, “Single-photon entanglement concentration for long-distance quantum communication,” Quantum Inf. Comput. 10, 272–281 (2010).
  41. 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]
  42. 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]
  43. 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]
  44. Y. B. Sheng, F. G. Deng, and G. L. Long, “Complete hyperentangled-Bell-state analysis for quantum communication,” Phys. Rev. A 82, 032318 (2010).
    [CrossRef]
  45. P. Kok, H. Lee, and J. P. Dowling, “Single-photon quantum-nondemolition detectors constructed with linear optics and projective measurements,” Phys. Rev. A 66, 063814 (2002).
    [CrossRef]
  46. P. Kok, W. J. Munro, K. Nemoto, T. C. Ralph, J. P. Dowling, and G. J. Milburn, “Linear optical quantum computing with photonic qubits,” Rev. Mod. Phys. 79, 135–174 (2007).
    [CrossRef]
  47. C. Wang, Y. Zhang, and G. S. Jin, “Polarization-entanglement purification and concentration using cross-Kerr nonlinearity,” Quantum Inf. Comput. 11, 988–1002 (2011).
  48. H. Schmidt and A. Imamogdlu, “Giant Kerr nonlinearities obtained by electromagnetically induced transparency,” Opt. Lett. 21, 1936–1938 (1996).
    [CrossRef]
  49. W. J. Munro, K. Nemoto, R. G. Beausoleil, and T. P. Spiller, “High-efficiency quantum-nondemolition single-photon-number-resolving detector,” Phys. Rev. A 71, 033819 (2005).
    [CrossRef]
  50. T. Hirano, H. Yamanaka, M. Ashikaga, T. Konishi, and R. Namiki, “Quantum cryptography using pulsed homodyne detection,” Phys. Rev. A 68, 042331 (2003).
    [CrossRef]
  51. S. H. Sun, M. Gao, M. S. Jiang, C. Y. Li, and L. M. Liang, “Partially random phase attack to the practical two-way quantum-key-distribution system,” Phys. Rev. A 85, 032304 (2012).
    [CrossRef]

2012 (5)

F. Agnes and L. Norbert, “Symmetries in quantum key distribution and the connection between optimal attacks and optimal cloning,” Phys. Rev. A 85, 052310 (2012).
[CrossRef]

F. G. Deng, “Optimal nonlocal multipartite entanglement concentration based on projection measurements,” Phys. Rev. A 85, 022311 (2012).
[CrossRef]

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

S. H. Sun, M. Gao, M. S. Jiang, C. Y. Li, and L. M. Liang, “Partially random phase attack to the practical two-way quantum-key-distribution system,” Phys. Rev. A 85, 032304 (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 (5)

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]

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

C. Wang, Y. Zhang, and G. S. Jin, “Polarization-entanglement purification and concentration using cross-Kerr nonlinearity,” Quantum Inf. Comput. 11, 988–1002 (2011).

Y. N. Wang, H. D. Shi, L. Jing, X. J. Ren, L. Z. Mu, and H. Fan, “Unified universal quantum cloning machine and fidelities,” Phys. Rev. A 84, 034302 (2011).
[CrossRef]

X. Y. Pan, G. Q. Liu, L. L. Yang, and H. Fan, “Solid-state optimal phase-covariant quantum cloning machine,” Appl. Phys. Lett. 99, 051113 (2011).
[CrossRef]

2010 (3)

Y. B. Sheng and F. G. Deng, “Deterministic entanglement purification and complete nonlocal Bell-state analysis with hyperentanglement,” Phys. Rev. A 81, 032307 (2010).
[CrossRef]

Y. B. Sheng, F. G. Deng, and H. Y. Zhou, “Single-photon entanglement concentration for long-distance quantum communication,” Quantum Inf. Comput. 10, 272–281 (2010).

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

2009 (2)

Y. B. Sheng, F. G. Deng, B. K. Zhao, T. J. Wang, and H. Y. Zhou, “Multipartite entanglement purification with quantum nondemolition detectors,” Eur. Phys. J. D 55, 235–242 (2009).
[CrossRef]

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

2008 (5)

Y. B. Sheng, F. G. Deng, and H. Y. Zhou, “Efficient polarization-entanglement purification based on parametric down-conversion sources with cross-Kerr nonlinearity,” Phys. Rev. A 77, 042308 (2008).
[CrossRef]

X. H. Li, F. G. Deng, and H. Y. Zhou, “Efficient quantum key distribution over a collective noise channel,” Phys. Rev. A 78, 022321 (2008).
[CrossRef]

J. Fiurášek and N. J. Cerf, “Quantum cloning of a pair of orthogonally polarized photons with linear optics,” Phys. Rev. A 77, 052308 (2008).
[CrossRef]

M. Sabuncu, G. Leuchs, and U. L. Andersen, “Experimental continuous-variable cloning of partial quantum information,” Phys. Rev. A 78, 052312 (2008).
[CrossRef]

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

2007 (2)

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

H. W. Chen, X. Y. Zhou, D. Suter, and J. F. Du, “Experimental realization of 1→2 asymmetric phase-covariant quantum cloning,” Phys. Rev. A 75, 012317 (2007).
[CrossRef]

2005 (5)

J. F. Du, T. Durt, P. Zou, H. Li, L. C. Kwek, C. H. Lai, C. H. Oh, and A. Ekert, “Experimental quantum cloning with prior partial information,” Phys. Rev. Lett. 94, 040505 (2005).
[CrossRef]

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

X. G. Song, X. L. Feng, L. C. Kwek, and C. H. Oh, “Entanglement purification based on photonic polarization parity measurements,” J. Phys. B. At. Mol. Opt. Phys. 38, 2827–2832 (2005).
[CrossRef]

J. Fiurášek, R. Filip, and N. J. Cerf, “Highly asymmetric quantum cloning in arbitrary dimension,” Quantum Inf. Comput. 5, 583–592 (2005).

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

2004 (3)

F. G. Deng and G. L. Long, “Secure direct communication with a quantum one-time-pad,” Phys. Rev. A 69, 052319 (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]

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

2003 (3)

J. Fiurášek, “Optical implementations of the optimal phase-covariant quantum cloning machine,” Phys. Rev. A 67, 052314 (2003).
[CrossRef]

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

T. Hirano, H. Yamanaka, M. Ashikaga, T. Konishi, and R. Namiki, “Quantum cryptography using pulsed homodyne detection,” Phys. Rev. A 68, 042331 (2003).
[CrossRef]

2002 (5)

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

H. K. Cummins, C. Jones, A. Furze, N. F. Soffe, M. Mosca, J. M. Peach, and J. A. Jones, “Approximate quantum cloning with nuclear magnetic resonance,” Phys. Rev. Lett. 88, 187901 (2002).
[CrossRef]

A. L. Linares, C. Simon, J. C. Howell, and D. Bouwmeester, “Experimental quantum cloning of single photons,” Science 296, 712–714 (2002).
[CrossRef]

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

N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, “Quantum cryptography,” Rev. Mod. Phys. 74, 145–195 (2002).
[CrossRef]

2001 (2)

J. Fiurášek, “Optical implementation of continuous-variable quantum cloning machines,” Phys. Rev. Lett. 86, 4942–4945 (2001).
[CrossRef]

H. Fan, K. Matsumoto, X. B. Wang, and M. Wadati, “Quantum cloning machines for equatorial qubits,” Phys. Rev. A 65, 012304 (2001).
[CrossRef]

2000 (1)

D. Bruss, M. Cinchetti, G. M. D’Ariano, and C. Macchiavello, “Phase-covariant quantum cloning,” Phys. Rev. A 62, 012302 (2000).
[CrossRef]

1998 (2)

R. F. Werner, “Optimal cloning of pure states,” Phys. Rev. A 58, 1827–1832 (1998).
[CrossRef]

L. M. Duan and G. C. Guo, “Probabilistic cloning and identification of linearly independent quantum states,” Phys. Rev. Lett. 80, 4999–5002 (1998).
[CrossRef]

1996 (2)

V. Bužek and M. Hillery, “Quantum copying: beyond the no-cloning theorem,” Phys. Rev. A 54, 1844–1852 (1996).
[CrossRef]

H. Schmidt and A. Imamogdlu, “Giant Kerr nonlinearities obtained by electromagnetically induced transparency,” Opt. Lett. 21, 1936–1938 (1996).
[CrossRef]

1992 (1)

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

1991 (1)

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

1982 (2)

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

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

Agnes, F.

F. Agnes and L. Norbert, “Symmetries in quantum key distribution and the connection between optimal attacks and optimal cloning,” Phys. Rev. A 85, 052310 (2012).
[CrossRef]

Andersen, U. L.

M. Sabuncu, G. Leuchs, and U. L. Andersen, “Experimental continuous-variable cloning of partial quantum information,” Phys. Rev. A 78, 052312 (2008).
[CrossRef]

Ashikaga, M.

T. Hirano, H. Yamanaka, M. Ashikaga, T. Konishi, and R. Namiki, “Quantum cryptography using pulsed homodyne detection,” Phys. Rev. A 68, 042331 (2003).
[CrossRef]

Barrett, S. D.

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

Beausoleil, R. G.

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

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

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 the IEEE International Conference on Computers, Systems, and Signal Processing, Bangalore, India, (IEEE, 1984), pp. 175–179.

Bouwmeester, D.

A. L. Linares, C. Simon, J. C. Howell, and D. Bouwmeester, “Experimental quantum cloning of single photons,” Science 296, 712–714 (2002).
[CrossRef]

Brassard, G.

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

Bruss, D.

D. Bruss, M. Cinchetti, G. M. D’Ariano, and C. Macchiavello, “Phase-covariant quantum cloning,” Phys. Rev. A 62, 012302 (2000).
[CrossRef]

Bužek, V.

V. Bužek and M. Hillery, “Quantum copying: beyond the no-cloning theorem,” Phys. Rev. A 54, 1844–1852 (1996).
[CrossRef]

Cerf, N. J.

J. Fiurášek and N. J. Cerf, “Quantum cloning of a pair of orthogonally polarized photons with linear optics,” Phys. Rev. A 77, 052308 (2008).
[CrossRef]

J. Fiurášek, R. Filip, and N. J. Cerf, “Highly asymmetric quantum cloning in arbitrary dimension,” Quantum Inf. Comput. 5, 583–592 (2005).

Chen, H. W.

H. W. Chen, X. Y. Zhou, D. Suter, and J. F. Du, “Experimental realization of 1→2 asymmetric phase-covariant quantum cloning,” Phys. Rev. A 75, 012317 (2007).
[CrossRef]

Chuang, I. L.

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

Cinchetti, M.

D. Bruss, M. Cinchetti, G. M. D’Ariano, and C. Macchiavello, “Phase-covariant quantum cloning,” Phys. Rev. A 62, 012302 (2000).
[CrossRef]

Cummins, H. K.

H. K. Cummins, C. Jones, A. Furze, N. F. Soffe, M. Mosca, J. M. Peach, and J. A. Jones, “Approximate quantum cloning with nuclear magnetic resonance,” Phys. Rev. Lett. 88, 187901 (2002).
[CrossRef]

D’Ariano, G. M.

D. Bruss, M. Cinchetti, G. M. D’Ariano, and C. Macchiavello, “Phase-covariant quantum cloning,” Phys. Rev. A 62, 012302 (2000).
[CrossRef]

Deng, F. G.

F. G. Deng, “Optimal nonlocal multipartite entanglement concentration based on projection measurements,” Phys. Rev. A 85, 022311 (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]

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

Y. B. Sheng, F. G. Deng, and H. Y. Zhou, “Single-photon entanglement concentration for long-distance quantum communication,” Quantum Inf. Comput. 10, 272–281 (2010).

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

Y. B. Sheng and F. G. Deng, “Deterministic entanglement purification and complete nonlocal Bell-state analysis with hyperentanglement,” Phys. Rev. A 81, 032307 (2010).
[CrossRef]

Y. B. Sheng, F. G. Deng, B. K. Zhao, T. J. Wang, and H. Y. Zhou, “Multipartite entanglement purification with quantum nondemolition detectors,” Eur. Phys. J. D 55, 235–242 (2009).
[CrossRef]

Y. B. Sheng, F. G. Deng, and H. Y. Zhou, “Efficient polarization-entanglement purification based on parametric down-conversion sources with cross-Kerr nonlinearity,” Phys. Rev. A 77, 042308 (2008).
[CrossRef]

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

X. H. Li, F. G. Deng, and H. Y. Zhou, “Efficient quantum key distribution over a collective noise channel,” Phys. Rev. A 78, 022321 (2008).
[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]

F. G. Deng and G. L. Long, “Secure direct communication with a quantum one-time-pad,” Phys. Rev. A 69, 052319 (2004).
[CrossRef]

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

Dieks, D.

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

Dowling, J. P.

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

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

Du, F. F.

Du, J. F.

H. W. Chen, X. Y. Zhou, D. Suter, and J. F. Du, “Experimental realization of 1→2 asymmetric phase-covariant quantum cloning,” Phys. Rev. A 75, 012317 (2007).
[CrossRef]

J. F. Du, T. Durt, P. Zou, H. Li, L. C. Kwek, C. H. Lai, C. H. Oh, and A. Ekert, “Experimental quantum cloning with prior partial information,” Phys. Rev. Lett. 94, 040505 (2005).
[CrossRef]

Duan, L. M.

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Y. B. Sheng, F. G. Deng, B. K. Zhao, T. J. Wang, and H. Y. Zhou, “Multipartite entanglement purification with quantum nondemolition detectors,” Eur. Phys. J. D 55, 235–242 (2009).
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Figures (2)

Fig. 1.
Fig. 1.

Quantum circuit of the optimal universal cloning of the north hemisphere state. Input qubit and copy qubit entering routes 1 and 2, respectively. HWP, half-wave plate; PBS, polarization beam splitter; and BS, 50/50 beam splitter. Photons passing through route 2, 6, and 3 will put a phase shift θ, +θ, and +θ on the coherent beam under the cross-Kerr nonlinearity. σx is one of the Pauli operators that is operated on the photon. The QND is based on the result of homodyne measurement. The dashed curve marks the classical feed forward, which will transform different states into the state that we need in the scheme.

Fig. 2.
Fig. 2.

Theoretical probability distribution of the probe coherent state with total phase shifts 0 and ±θ(θ=102), which correspond to the dashed and the solid curve, respectively. The average photon number of the coherent state is 1010photon/plus.

Equations (13)

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|ψ=cosθ2|0+eiϕsinθ2|1.
U={|0000|+12(|01+|10)10|,θ[0,π/2],12(|01+|10)00|+|1110|,θ[π/2,π].
F(θ)={12sin2θ2+cos4θ2+24sin2θ,θ[0,π/2],12cos2θ2+sin4θ2+24sin2θ,θ[π/2,π].
HQND=χNsNp,
Uck|ϕs|αp=eiHQNDt/|ns|αp=|ns|αeinθp.
|ψi=α|Hi+β|Vi,
α|Hir3+β/2(|Hir5+|Vir6),
|Ψ=α|Hir3|Hcr2|αeiθ+α|Hir3|Vcr2|α+β/2(|Vir6|Hcr2|αeiθ+|Hir5|Vcr2|αeiθ)+β/2(|Hir5|Hcr2|α+|Vir6|Vcr2|α).
α/2|Hir8|Hcr7+β/2(|Hir8|Vcr7+|Vir8|Hcr7)+α/2|Hir9|Hcr7+β/2(|Hir9|Vcr7+|Vir9|Hcr7),
α/2|Hir8|Vcr7+β/2(|Hir8|Hcr7+|Vir8|Vcr7)+α/2|Hir9|Vcr7+β/2(|Hir9|Hcr7+|Vir9|Vcr7).
P(x,ϕ)=2πκ2exp[2(xλμscosϕ)2/κ2],
Pe0=2πκ2Xthexp[2(xλμs)2/κ2]dx=1.4×104,
Pe±θ=2πκ2Xth+exp[2(xλμscosθ)2/κ2]dx=7.3×104.

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