Estimation of photon counting statistics with imperfect detectors

doi:10.1088/1674-1056/27/7/074208

Abstract The study on photon counting statistics is of fundamental importance in quantum optics. We theoretically analyzed the imperfect detection of an arbitrary quantum state. We derived photon counting formulae for six typical quantum states (i.e., Fock, coherent, squeeze-vacuum, thermal, odd and even coherent states) with finite quantum efficiencies and dark counts based on multiple on/off detector arrays. We applied the formulae to the simulation of multiphoton number detections and obtained both the simulated and ideal photon number distributions of each state. A comparison between the results by using the fidelity and relative entropy was carried out to evaluate the detection scheme and help select detectors for different quantum states.

Keywords: fidelity on/off detector photon number detection relative entropy

Received: 05 March 2018
Revised: 11 April 2018
Accepted manuscript online:

PACS:

42.50.-p

(Quantum optics)

Fund: Project supported by the National Natural Science Foundation of China (Grant Nos. 61627820, 11674306, 61590932, and 61377048).

Corresponding Authors: Jun-Feng Song, Yong-Sheng Zhang
E-mail: songjf@jlu.edu.cn;yshzhang@ustc.edu.cn

Cite this article:

Xiao-Chuan Han(韩晓川), Dong-Wei Zhuang(庄东炜), Yu-Xuan Li(李雨轩), Jun-Feng Song(宋俊峰), Yong-Sheng Zhang(张永生) Estimation of photon counting statistics with imperfect detectors 2018 Chin. Phys. B 27 074208

[1]	Kervalishvili P J 2015 IEEE Seventh International Conference on Intelligent Computing and Information Systems, 12-14 Dec 2015, Cairo, Egypt p. 1
[2]	Spiller T P 2003 Materials Today 6 30
[3]	Erhard M, Fickler R, Krenn M and Zeilinger A 2018 Light:Science & Applications 7 17146
[4]	Caspani L, Xiong C, Eggleton B J, Bajoni D, Liscidini M, Galli M, Morandotti R and Moss D J 2017 Light:Science & Applications 6 e17100
[5]	Liu G Q and Pan X Y 2018 Chin Phys. B 27 020304
[6]	Okada M, Kan T, Fuwa M, Takeda S, Yoshikawa J I, Loock P V and Furusawa A 2017 Conference on Lasers and Electro-Optics Europe & European Quantum Electronics Conference, 25-29 Jun. 2017 Munich Germany 2017, p. 1-1
[7]	Djordjevic I B 2016 IEEE Photonics Journal 8 1
[8]	Bouwmeester D, Pan J W, Mattle K, Eibl M, Weinfurter H and Zeilinger A 1997 Nature 390 575
[9]	Liang Z F, Ma S L, Xue H T, Ding F, Liu J L and Tang F L 2018 Chin. Phys. B 27 016801
[10]	Lu F F and Wang C F 2016 Chin. Phys. Lett. 33 74202
[11]	Ren X Z, He S, Cong H L and Wang X W 2012 Acta Phys. Sin. 61 124207
[12]	Wakakuwa E, Soeda A and Murao M 2017 IEEE Transactions on Information Theory, p.1-1.
[13]	Helstrom C W 1969 Journal of Statistical Physics 1 231
[14]	Zhang J, Itzler M A, Zbinden H and Pan J W 2015 Light:Science & Applications 4 e286
[15]	MunroW, Nemoto K, Beausoleil R and Spiller T 2005 Phys. Rev. A 71 033819
[16]	Rosenberg D, Lita A E, Miller A J and Nam S W 2005 Phys. Rev. A 71 061803
[17]	Rohde P P 2005 Journal of Optics B:Quantum and Semiclassical Optics 7 82
[18]	Rohde P P, Webb J G, Huntington E H and Ralph T C 2007 New J. Phys. 9 233
[19]	Eisaman M, Fan J, Migdall A and Polyakov S V 2011 Review of Scientific Instruments 82 071101
[20]	Cova S, Ghioni M, Lacaita A, Samori C and Zappa F 1996 Appl. Opt. 35 1956
[21]	Sperling J, Vogel W and Agarwal G S 2012 Phys. Rev. A 85 023820
[22]	Hall B C 2013 Quantum Theory for Mathematicians (Berlin:Springer-Verlag) p. 53.
[23]	Adamchik V 1997 Journal of Computational and Applied Mathematics 79 119
[24]	Abramowitz M and Stegun I A (Ed.) 1972 Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables (9th printing) (Denver:Dream Books Company, LLC) p. 331
[25]	Cozzini M, Ionicioiu R and Zanard P 2007 Phys. Rev. B 76 104420
[26]	Callen H B 1998 Thermodynamics and an Introduction to Thermostatistics p. 27.
[27]	Tan Y Z and Wu C F 2003 Journal of Natural Resources 1 017 (in Chinese)
[28]	Kullback S and Leibler R A 1951 The Annals of Mathematical Statistics 22 79

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