Abstract

We demonstrate a sub-shot-noise-limit discrimination of on-off keyed coherent signals by an optimal displacement quantum receiver in which a superconducting transition edge sensor is installed. Use of a transition edge sensor and a fiber beam splitter realizes high total detection efficiency and high interference visibility of the receiver and the observed average error surpasses the shot-noise-limit in a wider range of the signal power. Our technique opens up a new technology for the sub-shot-noise-limit detection of coherent signals in optical communication channels.

© 2010 OSA

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References

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  1. C. W. Helstrom, Quantum Detection and Estimation Theory (Academic Press, New York, 1976)
  2. C. W. Helstrom, “Detection theory and quantum mechanics,” Inf. Control 10(3), 254–291 (1967).
    [CrossRef]
  3. S. Dolinar, “An optimal receiver for the binary coherent state quantum channel”, Research Laboratory of Electronics, MIT, Quarterly Progress Report No. 111, 1973 (unpublised), pp. 115–120.
  4. M. Sasaki and O. Hirota, “Optimum decision scheme with a unitary control process for binary quantum-state signals,” Phys. Rev. A 54(4), 2728–2736 (1996).
    [CrossRef] [PubMed]
  5. 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(2), 022320 (2008).
    [CrossRef]
  6. R. S. Kennedy, “A near-optimal receiver for the binary coherent state quantum channel,” Research Laboratory of Electronics, MIT, Quarterly Progress Report No. 108, 1973 (unpublished), pp. 219–225.
  7. R. L. Cook, P. J. Martin, and J. M. Geremia, “Optical coherent state discrimination using a closed-loop quantum measurement,” Nature 446(7137), 774–777 (2007).
    [CrossRef] [PubMed]
  8. 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(21), 210501 (2008).
    [CrossRef] [PubMed]
  9. A. E. Lita, A. J. Miller, and S. W. Nam, “Counting near-infrared single-photons with 95% efficiency,” Opt. Express 16(5), 3032–3040 (2008).
    [CrossRef] [PubMed]
  10. D. Rosenberg, J. W. Harrington, P. R. Rice, P. A. Hiskett, C. G. Peterson, R. J. Hughes, A. E. Lita, S. W. Nam, and J. E. Nordholt, “Long-Distance Decoy-State Quantum Key Distribution in Optical Fiber,” Phys. Rev. Lett. 98(1), 010503 (2007).
    [CrossRef] [PubMed]
  11. D. Rosenberg, S. W. Nam, P. A. Hiskett, C. G. Peterson, R. J. Hughes, J. E. Nordholt, A. E. Lita, and A. J. Miller, “Quantum key distribution at telecom wavelengths with noise-free detectors,” Appl. Phys. Lett. 88(2), 021108–021110 (2006).
    [CrossRef]
  12. G. Di Giuseppe, M. Atatüre, M. D. Shaw, A. V. Sergienko, B. E. Saleh, M. C. Teich, A. J. Miller, S. W. Nam, and J. Martinis, “Direct observation of photon pairs at a single output port of a beam-splitter interferometer,” Phys. Rev. A 68(6), 063817 (2003).
    [CrossRef]
  13. D. Fukuda, G. Fujii, T. Numata, A. Yoshizawa, H. Tsuchida, H. Fujino, H. Ishii, T. Itatani, S. Inoue, and T. Zama, “Photon number resolving detection with high speed and high quantum efficiency,” Metrologia 46(4), S288–S292 (2009).
    [CrossRef]

2009

D. Fukuda, G. Fujii, T. Numata, A. Yoshizawa, H. Tsuchida, H. Fujino, H. Ishii, T. Itatani, S. Inoue, and T. Zama, “Photon number resolving detection with high speed and high quantum efficiency,” Metrologia 46(4), S288–S292 (2009).
[CrossRef]

2008

A. E. Lita, A. J. Miller, and S. W. Nam, “Counting near-infrared single-photons with 95% efficiency,” Opt. Express 16(5), 3032–3040 (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(2), 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(21), 210501 (2008).
[CrossRef] [PubMed]

2007

D. Rosenberg, J. W. Harrington, P. R. Rice, P. A. Hiskett, C. G. Peterson, R. J. Hughes, A. E. Lita, S. W. Nam, and J. E. Nordholt, “Long-Distance Decoy-State Quantum Key Distribution in Optical Fiber,” Phys. Rev. Lett. 98(1), 010503 (2007).
[CrossRef] [PubMed]

R. L. Cook, P. J. Martin, and J. M. Geremia, “Optical coherent state discrimination using a closed-loop quantum measurement,” Nature 446(7137), 774–777 (2007).
[CrossRef] [PubMed]

2006

D. Rosenberg, S. W. Nam, P. A. Hiskett, C. G. Peterson, R. J. Hughes, J. E. Nordholt, A. E. Lita, and A. J. Miller, “Quantum key distribution at telecom wavelengths with noise-free detectors,” Appl. Phys. Lett. 88(2), 021108–021110 (2006).
[CrossRef]

2003

G. Di Giuseppe, M. Atatüre, M. D. Shaw, A. V. Sergienko, B. E. Saleh, M. C. Teich, A. J. Miller, S. W. Nam, and J. Martinis, “Direct observation of photon pairs at a single output port of a beam-splitter interferometer,” Phys. Rev. A 68(6), 063817 (2003).
[CrossRef]

1996

M. Sasaki and O. Hirota, “Optimum decision scheme with a unitary control process for binary quantum-state signals,” Phys. Rev. A 54(4), 2728–2736 (1996).
[CrossRef] [PubMed]

1967

C. W. Helstrom, “Detection theory and quantum mechanics,” Inf. Control 10(3), 254–291 (1967).
[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(21), 210501 (2008).
[CrossRef] [PubMed]

Atatüre, M.

G. Di Giuseppe, M. Atatüre, M. D. Shaw, A. V. Sergienko, B. E. Saleh, M. C. Teich, A. J. Miller, S. W. Nam, and J. Martinis, “Direct observation of photon pairs at a single output port of a beam-splitter interferometer,” Phys. Rev. A 68(6), 063817 (2003).
[CrossRef]

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(21), 210501 (2008).
[CrossRef] [PubMed]

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(7137), 774–777 (2007).
[CrossRef] [PubMed]

Di Giuseppe, G.

G. Di Giuseppe, M. Atatüre, M. D. Shaw, A. V. Sergienko, B. E. Saleh, M. C. Teich, A. J. Miller, S. W. Nam, and J. Martinis, “Direct observation of photon pairs at a single output port of a beam-splitter interferometer,” Phys. Rev. A 68(6), 063817 (2003).
[CrossRef]

Fujii, G.

D. Fukuda, G. Fujii, T. Numata, A. Yoshizawa, H. Tsuchida, H. Fujino, H. Ishii, T. Itatani, S. Inoue, and T. Zama, “Photon number resolving detection with high speed and high quantum efficiency,” Metrologia 46(4), S288–S292 (2009).
[CrossRef]

Fujino, H.

D. Fukuda, G. Fujii, T. Numata, A. Yoshizawa, H. Tsuchida, H. Fujino, H. Ishii, T. Itatani, S. Inoue, and T. Zama, “Photon number resolving detection with high speed and high quantum efficiency,” Metrologia 46(4), S288–S292 (2009).
[CrossRef]

Fukuda, D.

D. Fukuda, G. Fujii, T. Numata, A. Yoshizawa, H. Tsuchida, H. Fujino, H. Ishii, T. Itatani, S. Inoue, and T. Zama, “Photon number resolving detection with high speed and high quantum efficiency,” Metrologia 46(4), S288–S292 (2009).
[CrossRef]

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(7137), 774–777 (2007).
[CrossRef] [PubMed]

Harrington, J. W.

D. Rosenberg, J. W. Harrington, P. R. Rice, P. A. Hiskett, C. G. Peterson, R. J. Hughes, A. E. Lita, S. W. Nam, and J. E. Nordholt, “Long-Distance Decoy-State Quantum Key Distribution in Optical Fiber,” Phys. Rev. Lett. 98(1), 010503 (2007).
[CrossRef] [PubMed]

Helstrom, C. W.

C. W. Helstrom, “Detection theory and quantum mechanics,” Inf. Control 10(3), 254–291 (1967).
[CrossRef]

Hirota, O.

M. Sasaki and O. Hirota, “Optimum decision scheme with a unitary control process for binary quantum-state signals,” Phys. Rev. A 54(4), 2728–2736 (1996).
[CrossRef] [PubMed]

Hiskett, P. A.

D. Rosenberg, J. W. Harrington, P. R. Rice, P. A. Hiskett, C. G. Peterson, R. J. Hughes, A. E. Lita, S. W. Nam, and J. E. Nordholt, “Long-Distance Decoy-State Quantum Key Distribution in Optical Fiber,” Phys. Rev. Lett. 98(1), 010503 (2007).
[CrossRef] [PubMed]

D. Rosenberg, S. W. Nam, P. A. Hiskett, C. G. Peterson, R. J. Hughes, J. E. Nordholt, A. E. Lita, and A. J. Miller, “Quantum key distribution at telecom wavelengths with noise-free detectors,” Appl. Phys. Lett. 88(2), 021108–021110 (2006).
[CrossRef]

Hughes, R. J.

D. Rosenberg, J. W. Harrington, P. R. Rice, P. A. Hiskett, C. G. Peterson, R. J. Hughes, A. E. Lita, S. W. Nam, and J. E. Nordholt, “Long-Distance Decoy-State Quantum Key Distribution in Optical Fiber,” Phys. Rev. Lett. 98(1), 010503 (2007).
[CrossRef] [PubMed]

D. Rosenberg, S. W. Nam, P. A. Hiskett, C. G. Peterson, R. J. Hughes, J. E. Nordholt, A. E. Lita, and A. J. Miller, “Quantum key distribution at telecom wavelengths with noise-free detectors,” Appl. Phys. Lett. 88(2), 021108–021110 (2006).
[CrossRef]

Inoue, S.

D. Fukuda, G. Fujii, T. Numata, A. Yoshizawa, H. Tsuchida, H. Fujino, H. Ishii, T. Itatani, S. Inoue, and T. Zama, “Photon number resolving detection with high speed and high quantum efficiency,” Metrologia 46(4), S288–S292 (2009).
[CrossRef]

Ishii, H.

D. Fukuda, G. Fujii, T. Numata, A. Yoshizawa, H. Tsuchida, H. Fujino, H. Ishii, T. Itatani, S. Inoue, and T. Zama, “Photon number resolving detection with high speed and high quantum efficiency,” Metrologia 46(4), S288–S292 (2009).
[CrossRef]

Itatani, T.

D. Fukuda, G. Fujii, T. Numata, A. Yoshizawa, H. Tsuchida, H. Fujino, H. Ishii, T. Itatani, S. Inoue, and T. Zama, “Photon number resolving detection with high speed and high quantum efficiency,” Metrologia 46(4), S288–S292 (2009).
[CrossRef]

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(21), 210501 (2008).
[CrossRef] [PubMed]

Lita, A. E.

A. E. Lita, A. J. Miller, and S. W. Nam, “Counting near-infrared single-photons with 95% efficiency,” Opt. Express 16(5), 3032–3040 (2008).
[CrossRef] [PubMed]

D. Rosenberg, J. W. Harrington, P. R. Rice, P. A. Hiskett, C. G. Peterson, R. J. Hughes, A. E. Lita, S. W. Nam, and J. E. Nordholt, “Long-Distance Decoy-State Quantum Key Distribution in Optical Fiber,” Phys. Rev. Lett. 98(1), 010503 (2007).
[CrossRef] [PubMed]

D. Rosenberg, S. W. Nam, P. A. Hiskett, C. G. Peterson, R. J. Hughes, J. E. Nordholt, A. E. Lita, and A. J. Miller, “Quantum key distribution at telecom wavelengths with noise-free detectors,” Appl. Phys. Lett. 88(2), 021108–021110 (2006).
[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(7137), 774–777 (2007).
[CrossRef] [PubMed]

Martinis, J.

G. Di Giuseppe, M. Atatüre, M. D. Shaw, A. V. Sergienko, B. E. Saleh, M. C. Teich, A. J. Miller, S. W. Nam, and J. Martinis, “Direct observation of photon pairs at a single output port of a beam-splitter interferometer,” Phys. Rev. A 68(6), 063817 (2003).
[CrossRef]

Miller, A. J.

A. E. Lita, A. J. Miller, and S. W. Nam, “Counting near-infrared single-photons with 95% efficiency,” Opt. Express 16(5), 3032–3040 (2008).
[CrossRef] [PubMed]

D. Rosenberg, S. W. Nam, P. A. Hiskett, C. G. Peterson, R. J. Hughes, J. E. Nordholt, A. E. Lita, and A. J. Miller, “Quantum key distribution at telecom wavelengths with noise-free detectors,” Appl. Phys. Lett. 88(2), 021108–021110 (2006).
[CrossRef]

G. Di Giuseppe, M. Atatüre, M. D. Shaw, A. V. Sergienko, B. E. Saleh, M. C. Teich, A. J. Miller, S. W. Nam, and J. Martinis, “Direct observation of photon pairs at a single output port of a beam-splitter interferometer,” Phys. Rev. A 68(6), 063817 (2003).
[CrossRef]

Nam, S. W.

A. E. Lita, A. J. Miller, and S. W. Nam, “Counting near-infrared single-photons with 95% efficiency,” Opt. Express 16(5), 3032–3040 (2008).
[CrossRef] [PubMed]

D. Rosenberg, J. W. Harrington, P. R. Rice, P. A. Hiskett, C. G. Peterson, R. J. Hughes, A. E. Lita, S. W. Nam, and J. E. Nordholt, “Long-Distance Decoy-State Quantum Key Distribution in Optical Fiber,” Phys. Rev. Lett. 98(1), 010503 (2007).
[CrossRef] [PubMed]

D. Rosenberg, S. W. Nam, P. A. Hiskett, C. G. Peterson, R. J. Hughes, J. E. Nordholt, A. E. Lita, and A. J. Miller, “Quantum key distribution at telecom wavelengths with noise-free detectors,” Appl. Phys. Lett. 88(2), 021108–021110 (2006).
[CrossRef]

G. Di Giuseppe, M. Atatüre, M. D. Shaw, A. V. Sergienko, B. E. Saleh, M. C. Teich, A. J. Miller, S. W. Nam, and J. Martinis, “Direct observation of photon pairs at a single output port of a beam-splitter interferometer,” Phys. Rev. A 68(6), 063817 (2003).
[CrossRef]

Nordholt, J. E.

D. Rosenberg, J. W. Harrington, P. R. Rice, P. A. Hiskett, C. G. Peterson, R. J. Hughes, A. E. Lita, S. W. Nam, and J. E. Nordholt, “Long-Distance Decoy-State Quantum Key Distribution in Optical Fiber,” Phys. Rev. Lett. 98(1), 010503 (2007).
[CrossRef] [PubMed]

D. Rosenberg, S. W. Nam, P. A. Hiskett, C. G. Peterson, R. J. Hughes, J. E. Nordholt, A. E. Lita, and A. J. Miller, “Quantum key distribution at telecom wavelengths with noise-free detectors,” Appl. Phys. Lett. 88(2), 021108–021110 (2006).
[CrossRef]

Numata, T.

D. Fukuda, G. Fujii, T. Numata, A. Yoshizawa, H. Tsuchida, H. Fujino, H. Ishii, T. Itatani, S. Inoue, and T. Zama, “Photon number resolving detection with high speed and high quantum efficiency,” Metrologia 46(4), S288–S292 (2009).
[CrossRef]

Peterson, C. G.

D. Rosenberg, J. W. Harrington, P. R. Rice, P. A. Hiskett, C. G. Peterson, R. J. Hughes, A. E. Lita, S. W. Nam, and J. E. Nordholt, “Long-Distance Decoy-State Quantum Key Distribution in Optical Fiber,” Phys. Rev. Lett. 98(1), 010503 (2007).
[CrossRef] [PubMed]

D. Rosenberg, S. W. Nam, P. A. Hiskett, C. G. Peterson, R. J. Hughes, J. E. Nordholt, A. E. Lita, and A. J. Miller, “Quantum key distribution at telecom wavelengths with noise-free detectors,” Appl. Phys. Lett. 88(2), 021108–021110 (2006).
[CrossRef]

Rice, P. R.

D. Rosenberg, J. W. Harrington, P. R. Rice, P. A. Hiskett, C. G. Peterson, R. J. Hughes, A. E. Lita, S. W. Nam, and J. E. Nordholt, “Long-Distance Decoy-State Quantum Key Distribution in Optical Fiber,” Phys. Rev. Lett. 98(1), 010503 (2007).
[CrossRef] [PubMed]

Rosenberg, D.

D. Rosenberg, J. W. Harrington, P. R. Rice, P. A. Hiskett, C. G. Peterson, R. J. Hughes, A. E. Lita, S. W. Nam, and J. E. Nordholt, “Long-Distance Decoy-State Quantum Key Distribution in Optical Fiber,” Phys. Rev. Lett. 98(1), 010503 (2007).
[CrossRef] [PubMed]

D. Rosenberg, S. W. Nam, P. A. Hiskett, C. G. Peterson, R. J. Hughes, J. E. Nordholt, A. E. Lita, and A. J. Miller, “Quantum key distribution at telecom wavelengths with noise-free detectors,” Appl. Phys. Lett. 88(2), 021108–021110 (2006).
[CrossRef]

Saleh, B. E.

G. Di Giuseppe, M. Atatüre, M. D. Shaw, A. V. Sergienko, B. E. Saleh, M. C. Teich, A. J. Miller, S. W. Nam, and J. Martinis, “Direct observation of photon pairs at a single output port of a beam-splitter interferometer,” Phys. Rev. A 68(6), 063817 (2003).
[CrossRef]

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(21), 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(2), 022320 (2008).
[CrossRef]

M. Sasaki and O. Hirota, “Optimum decision scheme with a unitary control process for binary quantum-state signals,” Phys. Rev. A 54(4), 2728–2736 (1996).
[CrossRef] [PubMed]

Sergienko, A. V.

G. Di Giuseppe, M. Atatüre, M. D. Shaw, A. V. Sergienko, B. E. Saleh, M. C. Teich, A. J. Miller, S. W. Nam, and J. Martinis, “Direct observation of photon pairs at a single output port of a beam-splitter interferometer,” Phys. Rev. A 68(6), 063817 (2003).
[CrossRef]

Shaw, M. D.

G. Di Giuseppe, M. Atatüre, M. D. Shaw, A. V. Sergienko, B. E. Saleh, M. C. Teich, A. J. Miller, S. W. Nam, and J. Martinis, “Direct observation of photon pairs at a single output port of a beam-splitter interferometer,” Phys. Rev. A 68(6), 063817 (2003).
[CrossRef]

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(21), 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(2), 022320 (2008).
[CrossRef]

Teich, M. C.

G. Di Giuseppe, M. Atatüre, M. D. Shaw, A. V. Sergienko, B. E. Saleh, M. C. Teich, A. J. Miller, S. W. Nam, and J. Martinis, “Direct observation of photon pairs at a single output port of a beam-splitter interferometer,” Phys. Rev. A 68(6), 063817 (2003).
[CrossRef]

Tsuchida, H.

D. Fukuda, G. Fujii, T. Numata, A. Yoshizawa, H. Tsuchida, H. Fujino, H. Ishii, T. Itatani, S. Inoue, and T. Zama, “Photon number resolving detection with high speed and high quantum efficiency,” Metrologia 46(4), S288–S292 (2009).
[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(21), 210501 (2008).
[CrossRef] [PubMed]

Yoshizawa, A.

D. Fukuda, G. Fujii, T. Numata, A. Yoshizawa, H. Tsuchida, H. Fujino, H. Ishii, T. Itatani, S. Inoue, and T. Zama, “Photon number resolving detection with high speed and high quantum efficiency,” Metrologia 46(4), S288–S292 (2009).
[CrossRef]

Zama, T.

D. Fukuda, G. Fujii, T. Numata, A. Yoshizawa, H. Tsuchida, H. Fujino, H. Ishii, T. Itatani, S. Inoue, and T. Zama, “Photon number resolving detection with high speed and high quantum efficiency,” Metrologia 46(4), S288–S292 (2009).
[CrossRef]

Appl. Phys. Lett.

D. Rosenberg, S. W. Nam, P. A. Hiskett, C. G. Peterson, R. J. Hughes, J. E. Nordholt, A. E. Lita, and A. J. Miller, “Quantum key distribution at telecom wavelengths with noise-free detectors,” Appl. Phys. Lett. 88(2), 021108–021110 (2006).
[CrossRef]

Inf. Control

C. W. Helstrom, “Detection theory and quantum mechanics,” Inf. Control 10(3), 254–291 (1967).
[CrossRef]

Metrologia

D. Fukuda, G. Fujii, T. Numata, A. Yoshizawa, H. Tsuchida, H. Fujino, H. Ishii, T. Itatani, S. Inoue, and T. Zama, “Photon number resolving detection with high speed and high quantum efficiency,” Metrologia 46(4), S288–S292 (2009).
[CrossRef]

Nature

R. L. Cook, P. J. Martin, and J. M. Geremia, “Optical coherent state discrimination using a closed-loop quantum measurement,” Nature 446(7137), 774–777 (2007).
[CrossRef] [PubMed]

Opt. Express

Phys. Rev. A

G. Di Giuseppe, M. Atatüre, M. D. Shaw, A. V. Sergienko, B. E. Saleh, M. C. Teich, A. J. Miller, S. W. Nam, and J. Martinis, “Direct observation of photon pairs at a single output port of a beam-splitter interferometer,” Phys. Rev. A 68(6), 063817 (2003).
[CrossRef]

M. Sasaki and O. Hirota, “Optimum decision scheme with a unitary control process for binary quantum-state signals,” Phys. Rev. A 54(4), 2728–2736 (1996).
[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(2), 022320 (2008).
[CrossRef]

Phys. Rev. Lett.

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(21), 210501 (2008).
[CrossRef] [PubMed]

D. Rosenberg, J. W. Harrington, P. R. Rice, P. A. Hiskett, C. G. Peterson, R. J. Hughes, A. E. Lita, S. W. Nam, and J. E. Nordholt, “Long-Distance Decoy-State Quantum Key Distribution in Optical Fiber,” Phys. Rev. Lett. 98(1), 010503 (2007).
[CrossRef] [PubMed]

Other

R. S. Kennedy, “A near-optimal receiver for the binary coherent state quantum channel,” Research Laboratory of Electronics, MIT, Quarterly Progress Report No. 108, 1973 (unpublished), pp. 219–225.

S. Dolinar, “An optimal receiver for the binary coherent state quantum channel”, Research Laboratory of Electronics, MIT, Quarterly Progress Report No. 111, 1973 (unpublised), pp. 115–120.

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

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Figures (6)

Fig. 1
Fig. 1

Schematic diagram of the optimal displacement receiver.

Fig. 2
Fig. 2

(a) Error probabilities as a function of displacement β. p(α|0) (p(0|α)) is the probability of incorrectly guessing | α ( | 0 ) . |α|2 = 0.6, η = 1, ν = 0, ξ = 1, and τ 1 . (b) Comparison of the average error probabilities of the shot-noise-limit (blue), the quantum-limit (black) and the optimal displacement receiver (red) with η = 0.55, 0.7, 0.9, and 1 (dotted-dashed, dotted, dashed, and solid lines). ν = 0, ξ = 1, and τ 1 .

Fig. 3
Fig. 3

Histogram of the pulse height distribution of the TES. The TES is irradiated by 20ns laser pulses at 853nm. The peaks correspond to different numbers of the photons detected. The Gaussian-like noise at each peak is 0.28 times of the single-photon energy at 853nm. The threshold for discriminating zero and non-zero photons (on-off detection) is indicated by the red allow.

Fig. 4
Fig. 4

Experimental setup. AM: amplitude modulator, BS: beam splitter, FBS: fiber beam splitter, PZT: piezo-transducer, TES: titanium superconducting transition edge sensor.

Fig. 5
Fig. 5

Photon number distribution of the signal states measured by the TES. The bars represent directly observed photon numbers and the circles are the Poissonian distribution with the average photon number of (a) n ¯ = 0.182 , (b) n ¯ = 0.441 , (c) n ¯ = 0.679 , and (d) n ¯ = 1.13 . Here n ¯ is experimentally estimated from N 0/N All.

Fig. 6
Fig. 6

Experimental results. (a) Error probabilities p(α|0) (squares), p(0|α) (triangles), and their averages (circles) for various β. |α|2 = 0.57. (b) The average error probabilities with our optimal displacement receiver. The red dotted line indicates a theoretical curve of the receiver with η = 0.7, ν = 0.02, ξ = 0.99, and τ = 0.99. In both figures, the plots are obtained by 8000 measurements for each signal with statistical error bars.

Equations (4)

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p e S N L = 1 2 ( α | Π ^ O F F | α + 0 | Π ^ O N | 0 ) = 1 2 e | α | 2
p e Q L = 1 2 ( 1 1 e | α | 2 )
p e O D R = 1 2 [ 1 e ν η | β | 2 { 1 exp [ η ( τ | α | 2 + 2 ξ τ α β ) ] } ]
Poisson( n ) = n ¯ n n ! exp ( n ¯ ) × N All

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