Abstract

We propose a secure quantum key distribution (QKD) protocol using a single not-so-weak coherent qubit. With two preprocesses for random rotation and compensation, a key bit is encoded to a randomly polarized not-so-weak coherent qubit. We analyze the security of the QKD protocol, which counters the photon number splitting and the impersonation attacks. The estimated mean number of photon, which is less than 6.0, guarantees security. Additionally, we discuss the possibility of quantum secure direct communication.

© 2007 Optical Society of America

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  1. C. H. Bennett and G. Brassard, in Proceedings of the IEEE International Conference on Computers, Systems and Signal Processing (IEEE, 1984), pp. 175-179.
  2. A. K. Ekert, Phys. Rev. Lett. 67, 661 (1991).
    [CrossRef] [PubMed]
  3. For a review, see N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, Rev. Mod. Phys. 74, 145 (2002).
    [CrossRef]
  4. C. H. Bennett, Phys. Rev. Lett. 68, 3121 (1992).
    [CrossRef] [PubMed]
  5. M. Curty, M. Lewenstein, and N. Lútkenhaus, Phys. Rev. Lett. 92, 217903 (2004).
    [CrossRef] [PubMed]
  6. F. Grosshans, G. Van Assche, J. Wenger, R. Brouri, N. J. Cerf, and P. Grangier, Nature 421, 238 (2003).
    [CrossRef] [PubMed]
  7. K. Bostroem and T. Felbinger, Phys. Rev. Lett. 89, 187902 (2002).
    [CrossRef]
  8. F. G. Deng and G. L. Long, Phys. Rev. A 69, 052319 (2004).
    [CrossRef]
  9. F. G. Deng and G. L. Long, Phys. Rev. A 70, 012311 (2004).
    [CrossRef]
  10. T. Jennewein, C. Simon, G. Weihs, H. Weinfurter, and A. Zeilinger, Phys. Rev. Lett. 84, 4729 (2000).
    [CrossRef] [PubMed]
  11. C. Kurtsiefer, P. Zarda, M. Halder, H. Weinfurter, P. M. Gorman, P. R. Tapster, and J. G. Rarity, Nature 419, 450 (2002).
    [CrossRef] [PubMed]
  12. E. Waks, K. Inoue, C. Santori, D. Fattal, J. Vuckovic, G. S. Solomon, and Y. Yamamoto, Nature 420, 762 (2002).
    [CrossRef] [PubMed]
  13. W. H. Kye, C. M. Kim, M. S. Kim, and Y. J. Park, Phys. Rev. Lett. 95, 040501 (2005).
    [CrossRef] [PubMed]
  14. G. Brassard, N. Lutkenhaus, T. Mor, and B. C. Sanders, Phys. Rev. Lett. 85, 1330 (2000).
    [CrossRef] [PubMed]
  15. M. Dusek, O. Haderka, M. Hendrych, and R. Myska, Phys. Rev. A 60, 149 (1999).
    [CrossRef]
  16. Q. Zhang, X. B. Wang, Y. A. Chen, W.-Y. Hwang, T. Yang, and J.-W. Pan, Phys. Rev. Lett. 96, 078901 (2006).
    [CrossRef] [PubMed]
  17. C. M. Kim, Y. J. Choi, and Y. J. Park, arXiv.org e-Print archive, quant-ph/0603013, March 2, 2006.
  18. X. B. Wang, Q. Zhang, Y. A. Chen, W. Y. Hwang, M. Kim, and Z. W. Pan, arXiv.org e-Print archive, quant-ph/0603010, March 15, 2006.
  19. Y. J. Choi, Y. J. Park, and C. M. Kim, arXiv.org e-Print archive, quant-ph/0603145, February 7, 2007.
  20. A. Chefles, Phys. Rev. A 64, 062305 (2002).
    [CrossRef]
  21. A. Acín, N. Gisin, and V. Scarani, Phys. Rev. A 69, 012309 (2004).
    [CrossRef]
  22. M. Lucamarini and S. Mancini, Phys. Rev. Lett. 94, 140501 (2005).
    [CrossRef] [PubMed]

2006

Q. Zhang, X. B. Wang, Y. A. Chen, W.-Y. Hwang, T. Yang, and J.-W. Pan, Phys. Rev. Lett. 96, 078901 (2006).
[CrossRef] [PubMed]

2005

W. H. Kye, C. M. Kim, M. S. Kim, and Y. J. Park, Phys. Rev. Lett. 95, 040501 (2005).
[CrossRef] [PubMed]

M. Lucamarini and S. Mancini, Phys. Rev. Lett. 94, 140501 (2005).
[CrossRef] [PubMed]

2004

A. Acín, N. Gisin, and V. Scarani, Phys. Rev. A 69, 012309 (2004).
[CrossRef]

M. Curty, M. Lewenstein, and N. Lútkenhaus, Phys. Rev. Lett. 92, 217903 (2004).
[CrossRef] [PubMed]

F. G. Deng and G. L. Long, Phys. Rev. A 69, 052319 (2004).
[CrossRef]

F. G. Deng and G. L. Long, Phys. Rev. A 70, 012311 (2004).
[CrossRef]

2003

F. Grosshans, G. Van Assche, J. Wenger, R. Brouri, N. J. Cerf, and P. Grangier, Nature 421, 238 (2003).
[CrossRef] [PubMed]

2002

K. Bostroem and T. Felbinger, Phys. Rev. Lett. 89, 187902 (2002).
[CrossRef]

For a review, see N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, Rev. Mod. Phys. 74, 145 (2002).
[CrossRef]

C. Kurtsiefer, P. Zarda, M. Halder, H. Weinfurter, P. M. Gorman, P. R. Tapster, and J. G. Rarity, Nature 419, 450 (2002).
[CrossRef] [PubMed]

E. Waks, K. Inoue, C. Santori, D. Fattal, J. Vuckovic, G. S. Solomon, and Y. Yamamoto, Nature 420, 762 (2002).
[CrossRef] [PubMed]

A. Chefles, Phys. Rev. A 64, 062305 (2002).
[CrossRef]

2000

G. Brassard, N. Lutkenhaus, T. Mor, and B. C. Sanders, Phys. Rev. Lett. 85, 1330 (2000).
[CrossRef] [PubMed]

T. Jennewein, C. Simon, G. Weihs, H. Weinfurter, and A. Zeilinger, Phys. Rev. Lett. 84, 4729 (2000).
[CrossRef] [PubMed]

1999

M. Dusek, O. Haderka, M. Hendrych, and R. Myska, Phys. Rev. A 60, 149 (1999).
[CrossRef]

1992

C. H. Bennett, Phys. Rev. Lett. 68, 3121 (1992).
[CrossRef] [PubMed]

1991

A. K. Ekert, Phys. Rev. Lett. 67, 661 (1991).
[CrossRef] [PubMed]

Acín, A.

A. Acín, N. Gisin, and V. Scarani, Phys. Rev. A 69, 012309 (2004).
[CrossRef]

Bennett, C. H.

C. H. Bennett, Phys. Rev. Lett. 68, 3121 (1992).
[CrossRef] [PubMed]

C. H. Bennett and G. Brassard, in Proceedings of the IEEE International Conference on Computers, Systems and Signal Processing (IEEE, 1984), pp. 175-179.

Bostroem, K.

K. Bostroem and T. Felbinger, Phys. Rev. Lett. 89, 187902 (2002).
[CrossRef]

Brassard, G.

G. Brassard, N. Lutkenhaus, T. Mor, and B. C. Sanders, Phys. Rev. Lett. 85, 1330 (2000).
[CrossRef] [PubMed]

C. H. Bennett and G. Brassard, in Proceedings of the IEEE International Conference on Computers, Systems and Signal Processing (IEEE, 1984), pp. 175-179.

Brouri, R.

F. Grosshans, G. Van Assche, J. Wenger, R. Brouri, N. J. Cerf, and P. Grangier, Nature 421, 238 (2003).
[CrossRef] [PubMed]

Cerf, N. J.

F. Grosshans, G. Van Assche, J. Wenger, R. Brouri, N. J. Cerf, and P. Grangier, Nature 421, 238 (2003).
[CrossRef] [PubMed]

Chefles, A.

A. Chefles, Phys. Rev. A 64, 062305 (2002).
[CrossRef]

Chen, Y. A.

Q. Zhang, X. B. Wang, Y. A. Chen, W.-Y. Hwang, T. Yang, and J.-W. Pan, Phys. Rev. Lett. 96, 078901 (2006).
[CrossRef] [PubMed]

X. B. Wang, Q. Zhang, Y. A. Chen, W. Y. Hwang, M. Kim, and Z. W. Pan, arXiv.org e-Print archive, quant-ph/0603010, March 15, 2006.

Choi, Y. J.

Y. J. Choi, Y. J. Park, and C. M. Kim, arXiv.org e-Print archive, quant-ph/0603145, February 7, 2007.

C. M. Kim, Y. J. Choi, and Y. J. Park, arXiv.org e-Print archive, quant-ph/0603013, March 2, 2006.

Curty, M.

M. Curty, M. Lewenstein, and N. Lútkenhaus, Phys. Rev. Lett. 92, 217903 (2004).
[CrossRef] [PubMed]

Deng, F. G.

F. G. Deng and G. L. Long, Phys. Rev. A 70, 012311 (2004).
[CrossRef]

F. G. Deng and G. L. Long, Phys. Rev. A 69, 052319 (2004).
[CrossRef]

Dusek, M.

M. Dusek, O. Haderka, M. Hendrych, and R. Myska, Phys. Rev. A 60, 149 (1999).
[CrossRef]

Ekert, A. K.

A. K. Ekert, Phys. Rev. Lett. 67, 661 (1991).
[CrossRef] [PubMed]

Fattal, D.

E. Waks, K. Inoue, C. Santori, D. Fattal, J. Vuckovic, G. S. Solomon, and Y. Yamamoto, Nature 420, 762 (2002).
[CrossRef] [PubMed]

Felbinger, T.

K. Bostroem and T. Felbinger, Phys. Rev. Lett. 89, 187902 (2002).
[CrossRef]

Gisin, N.

A. Acín, N. Gisin, and V. Scarani, Phys. Rev. A 69, 012309 (2004).
[CrossRef]

For a review, see N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, Rev. Mod. Phys. 74, 145 (2002).
[CrossRef]

Gorman, P. M.

C. Kurtsiefer, P. Zarda, M. Halder, H. Weinfurter, P. M. Gorman, P. R. Tapster, and J. G. Rarity, Nature 419, 450 (2002).
[CrossRef] [PubMed]

Grangier, P.

F. Grosshans, G. Van Assche, J. Wenger, R. Brouri, N. J. Cerf, and P. Grangier, Nature 421, 238 (2003).
[CrossRef] [PubMed]

Grosshans, F.

F. Grosshans, G. Van Assche, J. Wenger, R. Brouri, N. J. Cerf, and P. Grangier, Nature 421, 238 (2003).
[CrossRef] [PubMed]

Haderka, O.

M. Dusek, O. Haderka, M. Hendrych, and R. Myska, Phys. Rev. A 60, 149 (1999).
[CrossRef]

Halder, M.

C. Kurtsiefer, P. Zarda, M. Halder, H. Weinfurter, P. M. Gorman, P. R. Tapster, and J. G. Rarity, Nature 419, 450 (2002).
[CrossRef] [PubMed]

Hendrych, M.

M. Dusek, O. Haderka, M. Hendrych, and R. Myska, Phys. Rev. A 60, 149 (1999).
[CrossRef]

Hwang, W. Y.

X. B. Wang, Q. Zhang, Y. A. Chen, W. Y. Hwang, M. Kim, and Z. W. Pan, arXiv.org e-Print archive, quant-ph/0603010, March 15, 2006.

Hwang, W.-Y.

Q. Zhang, X. B. Wang, Y. A. Chen, W.-Y. Hwang, T. Yang, and J.-W. Pan, Phys. Rev. Lett. 96, 078901 (2006).
[CrossRef] [PubMed]

Inoue, K.

E. Waks, K. Inoue, C. Santori, D. Fattal, J. Vuckovic, G. S. Solomon, and Y. Yamamoto, Nature 420, 762 (2002).
[CrossRef] [PubMed]

Jennewein, T.

T. Jennewein, C. Simon, G. Weihs, H. Weinfurter, and A. Zeilinger, Phys. Rev. Lett. 84, 4729 (2000).
[CrossRef] [PubMed]

Kim, C. M.

W. H. Kye, C. M. Kim, M. S. Kim, and Y. J. Park, Phys. Rev. Lett. 95, 040501 (2005).
[CrossRef] [PubMed]

Y. J. Choi, Y. J. Park, and C. M. Kim, arXiv.org e-Print archive, quant-ph/0603145, February 7, 2007.

C. M. Kim, Y. J. Choi, and Y. J. Park, arXiv.org e-Print archive, quant-ph/0603013, March 2, 2006.

Kim, M.

X. B. Wang, Q. Zhang, Y. A. Chen, W. Y. Hwang, M. Kim, and Z. W. Pan, arXiv.org e-Print archive, quant-ph/0603010, March 15, 2006.

Kim, M. S.

W. H. Kye, C. M. Kim, M. S. Kim, and Y. J. Park, Phys. Rev. Lett. 95, 040501 (2005).
[CrossRef] [PubMed]

Kurtsiefer, C.

C. Kurtsiefer, P. Zarda, M. Halder, H. Weinfurter, P. M. Gorman, P. R. Tapster, and J. G. Rarity, Nature 419, 450 (2002).
[CrossRef] [PubMed]

Kye, W. H.

W. H. Kye, C. M. Kim, M. S. Kim, and Y. J. Park, Phys. Rev. Lett. 95, 040501 (2005).
[CrossRef] [PubMed]

Lewenstein, M.

M. Curty, M. Lewenstein, and N. Lútkenhaus, Phys. Rev. Lett. 92, 217903 (2004).
[CrossRef] [PubMed]

Long, G. L.

F. G. Deng and G. L. Long, Phys. Rev. A 70, 012311 (2004).
[CrossRef]

F. G. Deng and G. L. Long, Phys. Rev. A 69, 052319 (2004).
[CrossRef]

Lucamarini, M.

M. Lucamarini and S. Mancini, Phys. Rev. Lett. 94, 140501 (2005).
[CrossRef] [PubMed]

Lutkenhaus, N.

G. Brassard, N. Lutkenhaus, T. Mor, and B. C. Sanders, Phys. Rev. Lett. 85, 1330 (2000).
[CrossRef] [PubMed]

Lútkenhaus, N.

M. Curty, M. Lewenstein, and N. Lútkenhaus, Phys. Rev. Lett. 92, 217903 (2004).
[CrossRef] [PubMed]

Mancini, S.

M. Lucamarini and S. Mancini, Phys. Rev. Lett. 94, 140501 (2005).
[CrossRef] [PubMed]

Mor, T.

G. Brassard, N. Lutkenhaus, T. Mor, and B. C. Sanders, Phys. Rev. Lett. 85, 1330 (2000).
[CrossRef] [PubMed]

Myska, R.

M. Dusek, O. Haderka, M. Hendrych, and R. Myska, Phys. Rev. A 60, 149 (1999).
[CrossRef]

Pan, J.-W.

Q. Zhang, X. B. Wang, Y. A. Chen, W.-Y. Hwang, T. Yang, and J.-W. Pan, Phys. Rev. Lett. 96, 078901 (2006).
[CrossRef] [PubMed]

Pan, Z. W.

X. B. Wang, Q. Zhang, Y. A. Chen, W. Y. Hwang, M. Kim, and Z. W. Pan, arXiv.org e-Print archive, quant-ph/0603010, March 15, 2006.

Park, Y. J.

W. H. Kye, C. M. Kim, M. S. Kim, and Y. J. Park, Phys. Rev. Lett. 95, 040501 (2005).
[CrossRef] [PubMed]

Y. J. Choi, Y. J. Park, and C. M. Kim, arXiv.org e-Print archive, quant-ph/0603145, February 7, 2007.

C. M. Kim, Y. J. Choi, and Y. J. Park, arXiv.org e-Print archive, quant-ph/0603013, March 2, 2006.

Rarity, J. G.

C. Kurtsiefer, P. Zarda, M. Halder, H. Weinfurter, P. M. Gorman, P. R. Tapster, and J. G. Rarity, Nature 419, 450 (2002).
[CrossRef] [PubMed]

Ribordy, G.

For a review, see N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, Rev. Mod. Phys. 74, 145 (2002).
[CrossRef]

Sanders, B. C.

G. Brassard, N. Lutkenhaus, T. Mor, and B. C. Sanders, Phys. Rev. Lett. 85, 1330 (2000).
[CrossRef] [PubMed]

Santori, C.

E. Waks, K. Inoue, C. Santori, D. Fattal, J. Vuckovic, G. S. Solomon, and Y. Yamamoto, Nature 420, 762 (2002).
[CrossRef] [PubMed]

Scarani, V.

A. Acín, N. Gisin, and V. Scarani, Phys. Rev. A 69, 012309 (2004).
[CrossRef]

Simon, C.

T. Jennewein, C. Simon, G. Weihs, H. Weinfurter, and A. Zeilinger, Phys. Rev. Lett. 84, 4729 (2000).
[CrossRef] [PubMed]

Solomon, G. S.

E. Waks, K. Inoue, C. Santori, D. Fattal, J. Vuckovic, G. S. Solomon, and Y. Yamamoto, Nature 420, 762 (2002).
[CrossRef] [PubMed]

Tapster, P. R.

C. Kurtsiefer, P. Zarda, M. Halder, H. Weinfurter, P. M. Gorman, P. R. Tapster, and J. G. Rarity, Nature 419, 450 (2002).
[CrossRef] [PubMed]

Tittel, W.

For a review, see N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, Rev. Mod. Phys. 74, 145 (2002).
[CrossRef]

Van Assche, G.

F. Grosshans, G. Van Assche, J. Wenger, R. Brouri, N. J. Cerf, and P. Grangier, Nature 421, 238 (2003).
[CrossRef] [PubMed]

Vuckovic, J.

E. Waks, K. Inoue, C. Santori, D. Fattal, J. Vuckovic, G. S. Solomon, and Y. Yamamoto, Nature 420, 762 (2002).
[CrossRef] [PubMed]

Waks, E.

E. Waks, K. Inoue, C. Santori, D. Fattal, J. Vuckovic, G. S. Solomon, and Y. Yamamoto, Nature 420, 762 (2002).
[CrossRef] [PubMed]

Wang, X. B.

Q. Zhang, X. B. Wang, Y. A. Chen, W.-Y. Hwang, T. Yang, and J.-W. Pan, Phys. Rev. Lett. 96, 078901 (2006).
[CrossRef] [PubMed]

X. B. Wang, Q. Zhang, Y. A. Chen, W. Y. Hwang, M. Kim, and Z. W. Pan, arXiv.org e-Print archive, quant-ph/0603010, March 15, 2006.

Weihs, G.

T. Jennewein, C. Simon, G. Weihs, H. Weinfurter, and A. Zeilinger, Phys. Rev. Lett. 84, 4729 (2000).
[CrossRef] [PubMed]

Weinfurter, H.

C. Kurtsiefer, P. Zarda, M. Halder, H. Weinfurter, P. M. Gorman, P. R. Tapster, and J. G. Rarity, Nature 419, 450 (2002).
[CrossRef] [PubMed]

T. Jennewein, C. Simon, G. Weihs, H. Weinfurter, and A. Zeilinger, Phys. Rev. Lett. 84, 4729 (2000).
[CrossRef] [PubMed]

Wenger, J.

F. Grosshans, G. Van Assche, J. Wenger, R. Brouri, N. J. Cerf, and P. Grangier, Nature 421, 238 (2003).
[CrossRef] [PubMed]

Yamamoto, Y.

E. Waks, K. Inoue, C. Santori, D. Fattal, J. Vuckovic, G. S. Solomon, and Y. Yamamoto, Nature 420, 762 (2002).
[CrossRef] [PubMed]

Yang, T.

Q. Zhang, X. B. Wang, Y. A. Chen, W.-Y. Hwang, T. Yang, and J.-W. Pan, Phys. Rev. Lett. 96, 078901 (2006).
[CrossRef] [PubMed]

Zarda, P.

C. Kurtsiefer, P. Zarda, M. Halder, H. Weinfurter, P. M. Gorman, P. R. Tapster, and J. G. Rarity, Nature 419, 450 (2002).
[CrossRef] [PubMed]

Zbinden, H.

For a review, see N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, Rev. Mod. Phys. 74, 145 (2002).
[CrossRef]

Zeilinger, A.

T. Jennewein, C. Simon, G. Weihs, H. Weinfurter, and A. Zeilinger, Phys. Rev. Lett. 84, 4729 (2000).
[CrossRef] [PubMed]

Zhang, Q.

Q. Zhang, X. B. Wang, Y. A. Chen, W.-Y. Hwang, T. Yang, and J.-W. Pan, Phys. Rev. Lett. 96, 078901 (2006).
[CrossRef] [PubMed]

X. B. Wang, Q. Zhang, Y. A. Chen, W. Y. Hwang, M. Kim, and Z. W. Pan, arXiv.org e-Print archive, quant-ph/0603010, March 15, 2006.

Nature

F. Grosshans, G. Van Assche, J. Wenger, R. Brouri, N. J. Cerf, and P. Grangier, Nature 421, 238 (2003).
[CrossRef] [PubMed]

C. Kurtsiefer, P. Zarda, M. Halder, H. Weinfurter, P. M. Gorman, P. R. Tapster, and J. G. Rarity, Nature 419, 450 (2002).
[CrossRef] [PubMed]

E. Waks, K. Inoue, C. Santori, D. Fattal, J. Vuckovic, G. S. Solomon, and Y. Yamamoto, Nature 420, 762 (2002).
[CrossRef] [PubMed]

Phys. Rev. A

M. Dusek, O. Haderka, M. Hendrych, and R. Myska, Phys. Rev. A 60, 149 (1999).
[CrossRef]

F. G. Deng and G. L. Long, Phys. Rev. A 69, 052319 (2004).
[CrossRef]

F. G. Deng and G. L. Long, Phys. Rev. A 70, 012311 (2004).
[CrossRef]

A. Chefles, Phys. Rev. A 64, 062305 (2002).
[CrossRef]

A. Acín, N. Gisin, and V. Scarani, Phys. Rev. A 69, 012309 (2004).
[CrossRef]

Phys. Rev. Lett.

M. Lucamarini and S. Mancini, Phys. Rev. Lett. 94, 140501 (2005).
[CrossRef] [PubMed]

T. Jennewein, C. Simon, G. Weihs, H. Weinfurter, and A. Zeilinger, Phys. Rev. Lett. 84, 4729 (2000).
[CrossRef] [PubMed]

K. Bostroem and T. Felbinger, Phys. Rev. Lett. 89, 187902 (2002).
[CrossRef]

A. K. Ekert, Phys. Rev. Lett. 67, 661 (1991).
[CrossRef] [PubMed]

C. H. Bennett, Phys. Rev. Lett. 68, 3121 (1992).
[CrossRef] [PubMed]

M. Curty, M. Lewenstein, and N. Lútkenhaus, Phys. Rev. Lett. 92, 217903 (2004).
[CrossRef] [PubMed]

Q. Zhang, X. B. Wang, Y. A. Chen, W.-Y. Hwang, T. Yang, and J.-W. Pan, Phys. Rev. Lett. 96, 078901 (2006).
[CrossRef] [PubMed]

W. H. Kye, C. M. Kim, M. S. Kim, and Y. J. Park, Phys. Rev. Lett. 95, 040501 (2005).
[CrossRef] [PubMed]

G. Brassard, N. Lutkenhaus, T. Mor, and B. C. Sanders, Phys. Rev. Lett. 85, 1330 (2000).
[CrossRef] [PubMed]

Rev. Mod. Phys.

For a review, see N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, Rev. Mod. Phys. 74, 145 (2002).
[CrossRef]

Other

C. M. Kim, Y. J. Choi, and Y. J. Park, arXiv.org e-Print archive, quant-ph/0603013, March 2, 2006.

X. B. Wang, Q. Zhang, Y. A. Chen, W. Y. Hwang, M. Kim, and Z. W. Pan, arXiv.org e-Print archive, quant-ph/0603010, March 15, 2006.

Y. J. Choi, Y. J. Park, and C. M. Kim, arXiv.org e-Print archive, quant-ph/0603145, February 7, 2007.

C. H. Bennett and G. Brassard, in Proceedings of the IEEE International Conference on Computers, Systems and Signal Processing (IEEE, 1984), pp. 175-179.

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Figures (2)

Fig. 1
Fig. 1

(a) Probability of discrimination with POVM depending on the photon number. (b) Probability depending on the four cases of the Poisson statistics: A, B, C, and D are μ = 2 , μ = 4 , μ = 6 , and μ = 8 , respectively.

Fig. 2
Fig. 2

Eve’s total discrimination probability depending on the mean photon μ.

Equations (3)

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

P d ( n ) = 1 ( 1 2 ) [ ( n 1 ) 2 ] ,
P E ( n , μ ) = P d ( n ) P p ( n , μ ) .
P t ( μ ) = n = 3 P E ( n , μ ) 1 P ( 0 , μ ) .

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