Abstract

We numerically evaluate the transmission rates of a single fiber with the wavelength-division-multiplexing (WDM) transmission of coherent signals with conventional homodyne-based (dyne-type) detections and various quantum detection strategies. We reveal the quantitative gap between these detection strategies especially in the quantum-limited region where the quantum noise seriously limits the transmission rate. For an extremely weak signal input power, there is a crucial gap between the capacity limit and the transmission rates of the WDM system with dyne-type detections. We show that this gap is filled by applying a collective square root detection (SRD) only for each channel, not necessary for quantum collective decoding among WDM channels.

© 2010 Optical Society of America

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    [CrossRef]
  2. H. Takahashi, “Information theory of quantum mechanical channels,” in “Advances in Communication Systems, A.Balahrishnan, ed. (1965),Vol. 1, pp. 227-3100 .
  3. P. Hausladen, R. Jozsa, B. Schumacher, M. Westmoreland, and W. K. Wootters, “Classical information capacity of a quantum channel,” Phys. Rev. A 54, 1869-1876 (1996).
    [CrossRef] [PubMed]
  4. B. Schumacher and M. D. Westmoreland, “Sending classical information via noisy quantum channels,” Phys. Rev. A 56, 131-138 (1997).
    [CrossRef]
  5. A. S. Holevo, “The capacity of the quantum channel with general signal states,” IEEE Trans. Inf. Theory 44, 269-273 (1998).
    [CrossRef]
  6. A. S. Holevo, M. Sohma, and O. Hirota, “Capacity of quantum gaussian channels,” Phys. Rev. A 59, 1820-1828 (1999).
    [CrossRef]
  7. A. S. Holevo and R. F. Werner, “Evaluating capacities of bosonic gaussian channels,” Phys. Rev. A 63, 032312 (2001).
    [CrossRef]
  8. V. Giovannetti, S. Lloyd, L. Maccone, and P. W. Shor, “Broadband channel capacities,” Phys. Rev. A 68, 062323 (2003).
    [CrossRef]
  9. V. Giovannetti, S. Guha, S. Lloyd, L. Maccone, J. H. Shapiro, and H. P. Yuen, “Classical capacity of the lossy bosonic channel: The exact solution,” Phys. Rev. Lett. 92, 027902 (2004).
    [CrossRef] [PubMed]
  10. K. Kato, M. Osaki, M. Sasaki, and O. Hirota, “Quantum detection and mutual information for QAM and PSK signals,” IEEE Trans. Commun. 47, 248-254 (1999).
    [CrossRef]
  11. R. S. Kennedy, “A near-optimum receiver for the binary coherent state quantum channel,” Res. Lab Electron., MIT, Quarterly Progress Rep. (1973), p. 219.
  12. S. Dolinar, “An optimum receiver for the binary coherent state quantum channel,” Res. Lab Electron., MIT, Quarterly Progress Rep. (1973), p. 115.
  13. M. Takeoka and M. Sasaki, “Discrimination of the binary coherent signal: Gaussian-operation limit and simple non-gaussian near-optimal receivers,” Phys. Rev. A 78, 022320 (2008).
    [CrossRef]
  14. C. W. Helstrom, Quantum Detection and Estimation Theory (Academic, 1976).
  15. R. L. Cook, P. J. Martin, and J. M. Geremia, “Optical coherent state discrimination using a closed-loop quantum measurement,” Nature 446, 774-777 (2007).
    [CrossRef] [PubMed]
  16. C. Wittmann, M. Takeoka, K. N. Cassemiro, M. Sasaki, G. Leuchs, and U. L. Andersen, “Demonstration of near-optimal discrimination of optical coherent states,” Phys. Rev. Lett. 101, 210501 (2008).
    [CrossRef] [PubMed]
  17. M. Sasaki, R. Momose, and O. Hirota, “Quantum detection for on-off keyed mixed-state signals with a small amount of thermal noise,” Phys. Rev. A 55, 3222-3225 (1997).
    [CrossRef]
  18. V. A. Vilnrotter and C.-W. Lau, “Quantum detection of binary and ternary signals in the presence of thermal noise fields,” The InterPlanetary Network Progress Report, Vol. 42(2002).
  19. G. Cariolaro and G. Pierobon, “Performance of quantum data transmission systems in the presence of thermal noise,” eprint arXiv:0904.1073 (2009). Accepted for publication in IEEE Trans. Commun..
  20. H. Kogelnik, “High capacity optical communications: Personal recollections,” IEEE J. Sel. Top. Quantum Electron. 6, 1279-1286 (2000).
    [CrossRef]
  21. P. Mitra and J. Stark, “Nonlinear limits to the information capacity of optical fibre communications,” Nature 411, 1027-1030 (2001).
    [CrossRef] [PubMed]
  22. H. P. Yuen and V. W. S. Chan, “Noise in homodyne and heterodyne detection,” Opt. Lett. 8, 177-179 (1983).
    [CrossRef] [PubMed]
  23. V. P. Belavkin, “Optimum distinction of nonorthogonal quantum signals,” Radio Eng. Electron. Phys. 20, 39-47 (1975).
  24. A. S. Holevo, “On capacity of a quantum communication channel,” Probl. Peredachi Inf. 15, 3-11 (1979). Translation in Probl. Inf. Transm. 15, 247-253 (1979).
  25. M. Ban, K. Kurokawa, R. Momose, and O. Hirota, “Optimum measurements for discrimination among symmetric quantum states and parameter estimation,” Int. J. Theor. Phys. 36, 1269-1288 (1997).
    [CrossRef]
  26. M. Nielsen and I. Chuang, Quantum Computation and Quantum Information (Cambridge Univ. Press, 2000).
  27. J. R. Buck, S. J. van Enk, and C. A. Fuchs, “Experimental proposal for achieving superadditive communication capacities with a binary quantum alphabet,” Phys. Rev. A 61, 032309 (2000).
    [CrossRef]
  28. M. Fujiwara, M. Takeoka, J. Mizuno, and M. Sasaki, “Exceeding the classical capacity limit in a quantum optical channel,” Phys. Rev. Lett. 90, 167906 (2003).
    [CrossRef] [PubMed]
  29. M. Takeoka, M. Fujiwara, J. Mizuno, and M. Sasaki, “Implementation of generalized quantum measurements: Superadditive quantum coding, accessible information extraction, and classical capacity limit,” Phys. Rev. A 69, 052329 (2004).
    [CrossRef]

2008

M. Takeoka and M. Sasaki, “Discrimination of the binary coherent signal: Gaussian-operation limit and simple non-gaussian near-optimal receivers,” Phys. Rev. A 78, 022320 (2008).
[CrossRef]

C. Wittmann, M. Takeoka, K. N. Cassemiro, M. Sasaki, G. Leuchs, and U. L. Andersen, “Demonstration of near-optimal discrimination of optical coherent states,” Phys. Rev. Lett. 101, 210501 (2008).
[CrossRef] [PubMed]

2007

R. L. Cook, P. J. Martin, and J. M. Geremia, “Optical coherent state discrimination using a closed-loop quantum measurement,” Nature 446, 774-777 (2007).
[CrossRef] [PubMed]

2004

V. Giovannetti, S. Guha, S. Lloyd, L. Maccone, J. H. Shapiro, and H. P. Yuen, “Classical capacity of the lossy bosonic channel: The exact solution,” Phys. Rev. Lett. 92, 027902 (2004).
[CrossRef] [PubMed]

M. Takeoka, M. Fujiwara, J. Mizuno, and M. Sasaki, “Implementation of generalized quantum measurements: Superadditive quantum coding, accessible information extraction, and classical capacity limit,” Phys. Rev. A 69, 052329 (2004).
[CrossRef]

2003

M. Fujiwara, M. Takeoka, J. Mizuno, and M. Sasaki, “Exceeding the classical capacity limit in a quantum optical channel,” Phys. Rev. Lett. 90, 167906 (2003).
[CrossRef] [PubMed]

V. Giovannetti, S. Lloyd, L. Maccone, and P. W. Shor, “Broadband channel capacities,” Phys. Rev. A 68, 062323 (2003).
[CrossRef]

2001

P. Mitra and J. Stark, “Nonlinear limits to the information capacity of optical fibre communications,” Nature 411, 1027-1030 (2001).
[CrossRef] [PubMed]

A. S. Holevo and R. F. Werner, “Evaluating capacities of bosonic gaussian channels,” Phys. Rev. A 63, 032312 (2001).
[CrossRef]

2000

H. Kogelnik, “High capacity optical communications: Personal recollections,” IEEE J. Sel. Top. Quantum Electron. 6, 1279-1286 (2000).
[CrossRef]

J. R. Buck, S. J. van Enk, and C. A. Fuchs, “Experimental proposal for achieving superadditive communication capacities with a binary quantum alphabet,” Phys. Rev. A 61, 032309 (2000).
[CrossRef]

1999

A. S. Holevo, M. Sohma, and O. Hirota, “Capacity of quantum gaussian channels,” Phys. Rev. A 59, 1820-1828 (1999).
[CrossRef]

K. Kato, M. Osaki, M. Sasaki, and O. Hirota, “Quantum detection and mutual information for QAM and PSK signals,” IEEE Trans. Commun. 47, 248-254 (1999).
[CrossRef]

1998

A. S. Holevo, “The capacity of the quantum channel with general signal states,” IEEE Trans. Inf. Theory 44, 269-273 (1998).
[CrossRef]

1997

B. Schumacher and M. D. Westmoreland, “Sending classical information via noisy quantum channels,” Phys. Rev. A 56, 131-138 (1997).
[CrossRef]

M. Sasaki, R. Momose, and O. Hirota, “Quantum detection for on-off keyed mixed-state signals with a small amount of thermal noise,” Phys. Rev. A 55, 3222-3225 (1997).
[CrossRef]

M. Ban, K. Kurokawa, R. Momose, and O. Hirota, “Optimum measurements for discrimination among symmetric quantum states and parameter estimation,” Int. J. Theor. Phys. 36, 1269-1288 (1997).
[CrossRef]

1996

P. Hausladen, R. Jozsa, B. Schumacher, M. Westmoreland, and W. K. Wootters, “Classical information capacity of a quantum channel,” Phys. Rev. A 54, 1869-1876 (1996).
[CrossRef] [PubMed]

1983

1979

A. S. Holevo, “On capacity of a quantum communication channel,” Probl. Peredachi Inf. 15, 3-11 (1979). Translation in Probl. Inf. Transm. 15, 247-253 (1979).

1975

V. P. Belavkin, “Optimum distinction of nonorthogonal quantum signals,” Radio Eng. Electron. Phys. 20, 39-47 (1975).

1962

J. P. Gordon, “Quantum effects in communication systems,” Proc. IRE 50, 1808-1908 (1962).
[CrossRef]

Andersen, U. L.

C. Wittmann, M. Takeoka, K. N. Cassemiro, M. Sasaki, G. Leuchs, and U. L. Andersen, “Demonstration of near-optimal discrimination of optical coherent states,” Phys. Rev. Lett. 101, 210501 (2008).
[CrossRef] [PubMed]

Ban, M.

M. Ban, K. Kurokawa, R. Momose, and O. Hirota, “Optimum measurements for discrimination among symmetric quantum states and parameter estimation,” Int. J. Theor. Phys. 36, 1269-1288 (1997).
[CrossRef]

Belavkin, V. P.

V. P. Belavkin, “Optimum distinction of nonorthogonal quantum signals,” Radio Eng. Electron. Phys. 20, 39-47 (1975).

Buck, J. R.

J. R. Buck, S. J. van Enk, and C. A. Fuchs, “Experimental proposal for achieving superadditive communication capacities with a binary quantum alphabet,” Phys. Rev. A 61, 032309 (2000).
[CrossRef]

Cariolaro, G.

G. Cariolaro and G. Pierobon, “Performance of quantum data transmission systems in the presence of thermal noise,” eprint arXiv:0904.1073 (2009). Accepted for publication in IEEE Trans. Commun..

Cassemiro, K. N.

C. Wittmann, M. Takeoka, K. N. Cassemiro, M. Sasaki, G. Leuchs, and U. L. Andersen, “Demonstration of near-optimal discrimination of optical coherent states,” Phys. Rev. Lett. 101, 210501 (2008).
[CrossRef] [PubMed]

Chan, V. W. S.

Chuang, I.

M. Nielsen and I. Chuang, Quantum Computation and Quantum Information (Cambridge Univ. Press, 2000).

Cook, R. L.

R. L. Cook, P. J. Martin, and J. M. Geremia, “Optical coherent state discrimination using a closed-loop quantum measurement,” Nature 446, 774-777 (2007).
[CrossRef] [PubMed]

Dolinar, S.

S. Dolinar, “An optimum receiver for the binary coherent state quantum channel,” Res. Lab Electron., MIT, Quarterly Progress Rep. (1973), p. 115.

Fuchs, C. A.

J. R. Buck, S. J. van Enk, and C. A. Fuchs, “Experimental proposal for achieving superadditive communication capacities with a binary quantum alphabet,” Phys. Rev. A 61, 032309 (2000).
[CrossRef]

Fujiwara, M.

M. Takeoka, M. Fujiwara, J. Mizuno, and M. Sasaki, “Implementation of generalized quantum measurements: Superadditive quantum coding, accessible information extraction, and classical capacity limit,” Phys. Rev. A 69, 052329 (2004).
[CrossRef]

M. Fujiwara, M. Takeoka, J. Mizuno, and M. Sasaki, “Exceeding the classical capacity limit in a quantum optical channel,” Phys. Rev. Lett. 90, 167906 (2003).
[CrossRef] [PubMed]

Geremia, J. M.

R. L. Cook, P. J. Martin, and J. M. Geremia, “Optical coherent state discrimination using a closed-loop quantum measurement,” Nature 446, 774-777 (2007).
[CrossRef] [PubMed]

Giovannetti, V.

V. Giovannetti, S. Guha, S. Lloyd, L. Maccone, J. H. Shapiro, and H. P. Yuen, “Classical capacity of the lossy bosonic channel: The exact solution,” Phys. Rev. Lett. 92, 027902 (2004).
[CrossRef] [PubMed]

V. Giovannetti, S. Lloyd, L. Maccone, and P. W. Shor, “Broadband channel capacities,” Phys. Rev. A 68, 062323 (2003).
[CrossRef]

Gordon, J. P.

J. P. Gordon, “Quantum effects in communication systems,” Proc. IRE 50, 1808-1908 (1962).
[CrossRef]

Guha, S.

V. Giovannetti, S. Guha, S. Lloyd, L. Maccone, J. H. Shapiro, and H. P. Yuen, “Classical capacity of the lossy bosonic channel: The exact solution,” Phys. Rev. Lett. 92, 027902 (2004).
[CrossRef] [PubMed]

Hausladen, P.

P. Hausladen, R. Jozsa, B. Schumacher, M. Westmoreland, and W. K. Wootters, “Classical information capacity of a quantum channel,” Phys. Rev. A 54, 1869-1876 (1996).
[CrossRef] [PubMed]

Helstrom, C. W.

C. W. Helstrom, Quantum Detection and Estimation Theory (Academic, 1976).

Hirota, O.

K. Kato, M. Osaki, M. Sasaki, and O. Hirota, “Quantum detection and mutual information for QAM and PSK signals,” IEEE Trans. Commun. 47, 248-254 (1999).
[CrossRef]

A. S. Holevo, M. Sohma, and O. Hirota, “Capacity of quantum gaussian channels,” Phys. Rev. A 59, 1820-1828 (1999).
[CrossRef]

M. Sasaki, R. Momose, and O. Hirota, “Quantum detection for on-off keyed mixed-state signals with a small amount of thermal noise,” Phys. Rev. A 55, 3222-3225 (1997).
[CrossRef]

M. Ban, K. Kurokawa, R. Momose, and O. Hirota, “Optimum measurements for discrimination among symmetric quantum states and parameter estimation,” Int. J. Theor. Phys. 36, 1269-1288 (1997).
[CrossRef]

Holevo, A. S.

A. S. Holevo and R. F. Werner, “Evaluating capacities of bosonic gaussian channels,” Phys. Rev. A 63, 032312 (2001).
[CrossRef]

A. S. Holevo, M. Sohma, and O. Hirota, “Capacity of quantum gaussian channels,” Phys. Rev. A 59, 1820-1828 (1999).
[CrossRef]

A. S. Holevo, “The capacity of the quantum channel with general signal states,” IEEE Trans. Inf. Theory 44, 269-273 (1998).
[CrossRef]

A. S. Holevo, “On capacity of a quantum communication channel,” Probl. Peredachi Inf. 15, 3-11 (1979). Translation in Probl. Inf. Transm. 15, 247-253 (1979).

Jozsa, R.

P. Hausladen, R. Jozsa, B. Schumacher, M. Westmoreland, and W. K. Wootters, “Classical information capacity of a quantum channel,” Phys. Rev. A 54, 1869-1876 (1996).
[CrossRef] [PubMed]

Kato, K.

K. Kato, M. Osaki, M. Sasaki, and O. Hirota, “Quantum detection and mutual information for QAM and PSK signals,” IEEE Trans. Commun. 47, 248-254 (1999).
[CrossRef]

Kennedy, R. S.

R. S. Kennedy, “A near-optimum receiver for the binary coherent state quantum channel,” Res. Lab Electron., MIT, Quarterly Progress Rep. (1973), p. 219.

Kogelnik, H.

H. Kogelnik, “High capacity optical communications: Personal recollections,” IEEE J. Sel. Top. Quantum Electron. 6, 1279-1286 (2000).
[CrossRef]

Kurokawa, K.

M. Ban, K. Kurokawa, R. Momose, and O. Hirota, “Optimum measurements for discrimination among symmetric quantum states and parameter estimation,” Int. J. Theor. Phys. 36, 1269-1288 (1997).
[CrossRef]

Lau, C.-W.

V. A. Vilnrotter and C.-W. Lau, “Quantum detection of binary and ternary signals in the presence of thermal noise fields,” The InterPlanetary Network Progress Report, Vol. 42(2002).

Leuchs, G.

C. Wittmann, M. Takeoka, K. N. Cassemiro, M. Sasaki, G. Leuchs, and U. L. Andersen, “Demonstration of near-optimal discrimination of optical coherent states,” Phys. Rev. Lett. 101, 210501 (2008).
[CrossRef] [PubMed]

Lloyd, S.

V. Giovannetti, S. Guha, S. Lloyd, L. Maccone, J. H. Shapiro, and H. P. Yuen, “Classical capacity of the lossy bosonic channel: The exact solution,” Phys. Rev. Lett. 92, 027902 (2004).
[CrossRef] [PubMed]

V. Giovannetti, S. Lloyd, L. Maccone, and P. W. Shor, “Broadband channel capacities,” Phys. Rev. A 68, 062323 (2003).
[CrossRef]

Maccone, L.

V. Giovannetti, S. Guha, S. Lloyd, L. Maccone, J. H. Shapiro, and H. P. Yuen, “Classical capacity of the lossy bosonic channel: The exact solution,” Phys. Rev. Lett. 92, 027902 (2004).
[CrossRef] [PubMed]

V. Giovannetti, S. Lloyd, L. Maccone, and P. W. Shor, “Broadband channel capacities,” Phys. Rev. A 68, 062323 (2003).
[CrossRef]

Martin, P. J.

R. L. Cook, P. J. Martin, and J. M. Geremia, “Optical coherent state discrimination using a closed-loop quantum measurement,” Nature 446, 774-777 (2007).
[CrossRef] [PubMed]

Mitra, P.

P. Mitra and J. Stark, “Nonlinear limits to the information capacity of optical fibre communications,” Nature 411, 1027-1030 (2001).
[CrossRef] [PubMed]

Mizuno, J.

M. Takeoka, M. Fujiwara, J. Mizuno, and M. Sasaki, “Implementation of generalized quantum measurements: Superadditive quantum coding, accessible information extraction, and classical capacity limit,” Phys. Rev. A 69, 052329 (2004).
[CrossRef]

M. Fujiwara, M. Takeoka, J. Mizuno, and M. Sasaki, “Exceeding the classical capacity limit in a quantum optical channel,” Phys. Rev. Lett. 90, 167906 (2003).
[CrossRef] [PubMed]

Momose, R.

M. Ban, K. Kurokawa, R. Momose, and O. Hirota, “Optimum measurements for discrimination among symmetric quantum states and parameter estimation,” Int. J. Theor. Phys. 36, 1269-1288 (1997).
[CrossRef]

M. Sasaki, R. Momose, and O. Hirota, “Quantum detection for on-off keyed mixed-state signals with a small amount of thermal noise,” Phys. Rev. A 55, 3222-3225 (1997).
[CrossRef]

Nielsen, M.

M. Nielsen and I. Chuang, Quantum Computation and Quantum Information (Cambridge Univ. Press, 2000).

Osaki, M.

K. Kato, M. Osaki, M. Sasaki, and O. Hirota, “Quantum detection and mutual information for QAM and PSK signals,” IEEE Trans. Commun. 47, 248-254 (1999).
[CrossRef]

Pierobon, G.

G. Cariolaro and G. Pierobon, “Performance of quantum data transmission systems in the presence of thermal noise,” eprint arXiv:0904.1073 (2009). Accepted for publication in IEEE Trans. Commun..

Sasaki, M.

C. Wittmann, M. Takeoka, K. N. Cassemiro, M. Sasaki, G. Leuchs, and U. L. Andersen, “Demonstration of near-optimal discrimination of optical coherent states,” Phys. Rev. Lett. 101, 210501 (2008).
[CrossRef] [PubMed]

M. Takeoka and M. Sasaki, “Discrimination of the binary coherent signal: Gaussian-operation limit and simple non-gaussian near-optimal receivers,” Phys. Rev. A 78, 022320 (2008).
[CrossRef]

M. Takeoka, M. Fujiwara, J. Mizuno, and M. Sasaki, “Implementation of generalized quantum measurements: Superadditive quantum coding, accessible information extraction, and classical capacity limit,” Phys. Rev. A 69, 052329 (2004).
[CrossRef]

M. Fujiwara, M. Takeoka, J. Mizuno, and M. Sasaki, “Exceeding the classical capacity limit in a quantum optical channel,” Phys. Rev. Lett. 90, 167906 (2003).
[CrossRef] [PubMed]

K. Kato, M. Osaki, M. Sasaki, and O. Hirota, “Quantum detection and mutual information for QAM and PSK signals,” IEEE Trans. Commun. 47, 248-254 (1999).
[CrossRef]

M. Sasaki, R. Momose, and O. Hirota, “Quantum detection for on-off keyed mixed-state signals with a small amount of thermal noise,” Phys. Rev. A 55, 3222-3225 (1997).
[CrossRef]

Schumacher, B.

B. Schumacher and M. D. Westmoreland, “Sending classical information via noisy quantum channels,” Phys. Rev. A 56, 131-138 (1997).
[CrossRef]

P. Hausladen, R. Jozsa, B. Schumacher, M. Westmoreland, and W. K. Wootters, “Classical information capacity of a quantum channel,” Phys. Rev. A 54, 1869-1876 (1996).
[CrossRef] [PubMed]

Shapiro, J. H.

V. Giovannetti, S. Guha, S. Lloyd, L. Maccone, J. H. Shapiro, and H. P. Yuen, “Classical capacity of the lossy bosonic channel: The exact solution,” Phys. Rev. Lett. 92, 027902 (2004).
[CrossRef] [PubMed]

Shor, P. W.

V. Giovannetti, S. Lloyd, L. Maccone, and P. W. Shor, “Broadband channel capacities,” Phys. Rev. A 68, 062323 (2003).
[CrossRef]

Sohma, M.

A. S. Holevo, M. Sohma, and O. Hirota, “Capacity of quantum gaussian channels,” Phys. Rev. A 59, 1820-1828 (1999).
[CrossRef]

Stark, J.

P. Mitra and J. Stark, “Nonlinear limits to the information capacity of optical fibre communications,” Nature 411, 1027-1030 (2001).
[CrossRef] [PubMed]

Takahashi, H.

H. Takahashi, “Information theory of quantum mechanical channels,” in “Advances in Communication Systems, A.Balahrishnan, ed. (1965),Vol. 1, pp. 227-3100 .

Takeoka, M.

C. Wittmann, M. Takeoka, K. N. Cassemiro, M. Sasaki, G. Leuchs, and U. L. Andersen, “Demonstration of near-optimal discrimination of optical coherent states,” Phys. Rev. Lett. 101, 210501 (2008).
[CrossRef] [PubMed]

M. Takeoka and M. Sasaki, “Discrimination of the binary coherent signal: Gaussian-operation limit and simple non-gaussian near-optimal receivers,” Phys. Rev. A 78, 022320 (2008).
[CrossRef]

M. Takeoka, M. Fujiwara, J. Mizuno, and M. Sasaki, “Implementation of generalized quantum measurements: Superadditive quantum coding, accessible information extraction, and classical capacity limit,” Phys. Rev. A 69, 052329 (2004).
[CrossRef]

M. Fujiwara, M. Takeoka, J. Mizuno, and M. Sasaki, “Exceeding the classical capacity limit in a quantum optical channel,” Phys. Rev. Lett. 90, 167906 (2003).
[CrossRef] [PubMed]

van Enk, S. J.

J. R. Buck, S. J. van Enk, and C. A. Fuchs, “Experimental proposal for achieving superadditive communication capacities with a binary quantum alphabet,” Phys. Rev. A 61, 032309 (2000).
[CrossRef]

Vilnrotter, V. A.

V. A. Vilnrotter and C.-W. Lau, “Quantum detection of binary and ternary signals in the presence of thermal noise fields,” The InterPlanetary Network Progress Report, Vol. 42(2002).

Werner, R. F.

A. S. Holevo and R. F. Werner, “Evaluating capacities of bosonic gaussian channels,” Phys. Rev. A 63, 032312 (2001).
[CrossRef]

Westmoreland, M.

P. Hausladen, R. Jozsa, B. Schumacher, M. Westmoreland, and W. K. Wootters, “Classical information capacity of a quantum channel,” Phys. Rev. A 54, 1869-1876 (1996).
[CrossRef] [PubMed]

Westmoreland, M. D.

B. Schumacher and M. D. Westmoreland, “Sending classical information via noisy quantum channels,” Phys. Rev. A 56, 131-138 (1997).
[CrossRef]

Wittmann, C.

C. Wittmann, M. Takeoka, K. N. Cassemiro, M. Sasaki, G. Leuchs, and U. L. Andersen, “Demonstration of near-optimal discrimination of optical coherent states,” Phys. Rev. Lett. 101, 210501 (2008).
[CrossRef] [PubMed]

Wootters, W. K.

P. Hausladen, R. Jozsa, B. Schumacher, M. Westmoreland, and W. K. Wootters, “Classical information capacity of a quantum channel,” Phys. Rev. A 54, 1869-1876 (1996).
[CrossRef] [PubMed]

Yuen, H. P.

V. Giovannetti, S. Guha, S. Lloyd, L. Maccone, J. H. Shapiro, and H. P. Yuen, “Classical capacity of the lossy bosonic channel: The exact solution,” Phys. Rev. Lett. 92, 027902 (2004).
[CrossRef] [PubMed]

H. P. Yuen and V. W. S. Chan, “Noise in homodyne and heterodyne detection,” Opt. Lett. 8, 177-179 (1983).
[CrossRef] [PubMed]

IEEE J. Sel. Top. Quantum Electron.

H. Kogelnik, “High capacity optical communications: Personal recollections,” IEEE J. Sel. Top. Quantum Electron. 6, 1279-1286 (2000).
[CrossRef]

IEEE Trans. Commun.

K. Kato, M. Osaki, M. Sasaki, and O. Hirota, “Quantum detection and mutual information for QAM and PSK signals,” IEEE Trans. Commun. 47, 248-254 (1999).
[CrossRef]

IEEE Trans. Inf. Theory

A. S. Holevo, “The capacity of the quantum channel with general signal states,” IEEE Trans. Inf. Theory 44, 269-273 (1998).
[CrossRef]

Int. J. Theor. Phys.

M. Ban, K. Kurokawa, R. Momose, and O. Hirota, “Optimum measurements for discrimination among symmetric quantum states and parameter estimation,” Int. J. Theor. Phys. 36, 1269-1288 (1997).
[CrossRef]

Nature

P. Mitra and J. Stark, “Nonlinear limits to the information capacity of optical fibre communications,” Nature 411, 1027-1030 (2001).
[CrossRef] [PubMed]

R. L. Cook, P. J. Martin, and J. M. Geremia, “Optical coherent state discrimination using a closed-loop quantum measurement,” Nature 446, 774-777 (2007).
[CrossRef] [PubMed]

Opt. Lett.

Phys. Rev. A

J. R. Buck, S. J. van Enk, and C. A. Fuchs, “Experimental proposal for achieving superadditive communication capacities with a binary quantum alphabet,” Phys. Rev. A 61, 032309 (2000).
[CrossRef]

M. Takeoka, M. Fujiwara, J. Mizuno, and M. Sasaki, “Implementation of generalized quantum measurements: Superadditive quantum coding, accessible information extraction, and classical capacity limit,” Phys. Rev. A 69, 052329 (2004).
[CrossRef]

M. Sasaki, R. Momose, and O. Hirota, “Quantum detection for on-off keyed mixed-state signals with a small amount of thermal noise,” Phys. Rev. A 55, 3222-3225 (1997).
[CrossRef]

M. Takeoka and M. Sasaki, “Discrimination of the binary coherent signal: Gaussian-operation limit and simple non-gaussian near-optimal receivers,” Phys. Rev. A 78, 022320 (2008).
[CrossRef]

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Figures (6)

Fig. 1
Fig. 1

Schematic of our coherent communication model.

Fig. 2
Fig. 2

Phase-space representation of the BPSK and 4PSK signals.

Fig. 3
Fig. 3

Phase-space representation of the signals with 9QAM and 16QAM.

Fig. 4
Fig. 4

Transmission rate T: theoretical limit given by Giovannetti, et al., (black) BPSK (blue) with homodyne detection, and 4PSK (red), 9QAM (green), 16QAM (purple), 36QAM (light blue), and 64QAM (brown) with heterodyne detection.

Fig. 5
Fig. 5

Ratio of transmission rate to theoretical limit: BPSK (blue) with homodyne detection and 4PSK (red), 9QAM (green), 16QAM (purple), 36QAM (light blue), and 64QAM (brown) with heterodyne detection.

Fig. 6
Fig. 6

(a) Transmission rate T of BPSK and 4PSK with various quantum detection strategies. (b) Ratio of transmission rate to theoretical limit: theoretical limit given by Giovannetti, et al. (black), BPSK with homodyne detection (blue), 4PSK with heterodyne detection (red), BPSK (light blue) and 4PSK (brown) with the single-shot square root detection, and BPSK (green) and 4PSK (purple) with the collective SRD.

Tables (2)

Tables Icon

Table 1 Notations and Parameters

Tables Icon

Table 2 Necessary Power and Transmission Rate for Entering the Classical Region

Equations (24)

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C = f L f U d f g ( η n ¯ ( f , β ) ) [ bit channel ] ,
n ¯ ( f , β ) = 1 η exp ( β h f η ) 1 ,
P = f L f U d f h f n ¯ ( f , β ) [ W ] .
| α = exp [ | α | 2 2 ] n = 0 α n n ! | n ,
n ¯ = 1 M i = 1 M | α i | 2 .
P = r × 1 M i = 1 M | α i | 2 h j = 1 n f j [ W ] ,
| φ i = | α exp [ 2 ( i 1 ) π i M ] ,
M = L 2 , L = 3 , 4 , 5 .
Ω = { ( L 1 ) + 2 ( i 1 ) | i = 1 , 2 , , L } .
| φ p q = | α ( p + i q ) , p , q Ω .
p ( x c ) = 2 π exp [ 2 ( x c α ) 2 ] .
p ( x c , x s ) = 1 π exp [ ( x c α 1 ) 2 ( x s α 2 ) 2 ] .
Π ̂ j = | μ j μ j | ,
| μ j = G ̂ 1 2 | ψ j ,
G ̂ = i = 1 S | ψ i ψ i | .
j = 1 S Π ̂ j = G ̂ 1 2 ( j = 1 M | ψ ψ | ) G ̂ 1 2 = G ̂ 1 2 G ̂ G ̂ 1 2 = I ̂ ,
P ( j | i ) = | ( G 1 2 ) j i | 2 ,
G = ( ψ 1 | ψ 1 ψ 1 | ψ 2 ψ 1 | ψ S ψ 2 | ψ 1 ψ 2 | ψ 2 ψ 2 | ψ S ψ S | ψ 1 ψ S | ψ 2 ψ S | ψ S ) .
I ( X ; Y ) = i X P ( i ) j Y P ( j | i ) log [ P ( j | i ) k X P ( k ) P ( j | k ) ] [ bit signal ] ,
T = n × r × I ( X ; Y ) [ bit s ] .
I ( p i , ρ i ) = S ( ρ ) i p i S ( ρ i ) [ bit signal ] ,
S ( ρ ) = i λ i log λ i ,
( p 1 p 1 ψ 1 | ψ 1 p 1 p 2 ψ 1 | ψ 2 p 1 p S ψ 1 | ψ S p 2 p 1 ψ 2 | ψ 1 p 2 p 2 ψ 2 | ψ 2 p 2 p S ψ 2 | ψ S p S p 1 ψ S | ψ 1 p S p 2 ψ S | ψ 2 p S p S ψ S | ψ S ) .
T = n × r × I [ bit s ] .

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