## Sub-shot-noise-limit discrimination of on-off keyed coherent signals via a quantum receiver with a superconducting transition edge sensor

Optics Express, Vol. 18, Issue 8, pp. 8107-8114 (2010)

http://dx.doi.org/10.1364/OE.18.008107

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### 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

## 1. Introduction

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

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]

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]

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]

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]

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]

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]

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]

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]

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]

**101**(21), 210501 (2008). [CrossRef] [PubMed]

## 2. Optimal displacement receiver

*p*and

_{α}*p*

_{0}, respectively. For simplicity, we assume

*n*-photon number state. The average error probability by the on-off detection, i.e. the shot-noise-limit, is calculated to bewhile the minimum error predicted by the quantum detection theory (quantum-limit) [1] is always lower than

*η*, the dark counts

*ν*, and the mode match factor between the signal and the local oscillator

*ξ*[5

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]

*β*is chosen such that

*β*. To illustrate the trade-off relation of each error, we plot the discrimination errors for the coherent state and the vacuum separately, which clearly suggests that the average error is minimized at certain

*β*. The average error with optimal

*β*for various |

*α*|

^{2}is shown in Fig. 2(b). In ideal, the optimal displacement receiver surpasses the shot-noise-limit for any |

*α*|

^{2}. We also plot the average errors for imperfect

*η*showing the drastic increase of errors with the decrease of

*η*.

## 3. Transition edge sensor as an on-off detector

*η*of the receiver as high as possible, we have used a TES as an on-off detector. Here we briefly describe our TES device and its operation as an on-off detector. TES is a calorimetric superconducting thermometer. The energy of absorbed photons at the TES film is sensed as the resistance increase and read out via a SQUID amplifier. Our TES consists of a

^{2}titanium superconductor (30nm thickness) which is cooled down to 100mK whose quantum efficiency is 73 ± 3% at 853nm including the fiber-to-detector coupling loss. TES has the photon number resolving ability. Figure 3 shows an example of the pulse height distribution of the output voltage from our TES under 853nm laser pulse irradiation where the photon numbers are clearly distinguished. The energy resolution of the pulse height distribution is 0.4 eV. Details of the TES and its calibration method are found in [13

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]

## 4. Results

*α*|

^{2}. We observe a nice coincidence and thus confirm that our signal source is classical noise-free. Calibration of the amplitude modulator for the signal state preparation (AM1) is also carried our by measuring the zero-photon count ratio.

*β*as shown in Fig. 6(a) . Each plot with an error bar is obtained by repeating 8000 measurements and the minimization of the average error probability at certain

*β*is observed. Figure 6(b) shows the experimental average error probabilities for various |

*α*|

^{2}. The displacement

*β*for each |

*α*|

^{2}is chosen to be optimal according to the numerical model mentioned above. The squares are the experimental results and clearly surpass the (theoretical) shot-noise-limit (blue line) up to

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]

## 5. Summary

**78**(2), 022320 (2008). [CrossRef]

## Acknowledgments

## References and links

1. | C. W. Helstrom, |

2. | C. W. Helstrom, “Detection theory and quantum mechanics,” Inf. Control |

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 |

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 |

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 |

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. |

9. | A. E. Lita, A. J. Miller, and S. W. Nam, “Counting near-infrared single-photons with 95% efficiency,” Opt. Express |

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. |

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. |

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 |

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 |

**OCIS Codes**

(270.0270) Quantum optics : Quantum optics

(270.5570) Quantum optics : Quantum detectors

**ToC Category:**

Quantum Optics

**History**

Original Manuscript: February 12, 2010

Revised Manuscript: March 11, 2010

Manuscript Accepted: March 20, 2010

Published: April 1, 2010

**Citation**

Kenji Tsujino, Daiji Fukuda, Go Fujii, Shuichiro Inoue, Mikio Fujiwara, Masahiro Takeoka, and Masahide Sasaki, "Sub-shot-noise-limit discrimination of on-off keyed coherent signals via a quantum receiver with a superconducting transition edge sensor," Opt. Express **18**, 8107-8114 (2010)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-18-8-8107

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### References

- C. W. Helstrom, Quantum Detection and Estimation Theory (Academic Press, New York, 1976)
- C. W. Helstrom, “Detection theory and quantum mechanics,” Inf. Control 10(3), 254–291 (1967). [CrossRef]
- 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.
- 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]
- 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.
- 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]
- 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]
- 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]
- 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]

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