Abstract

Discriminating between Fock states with a high degree of accuracy is a desirable feature for modern applications of optical quantum information processing. A well-known alternative to sophisticated photon number discriminating detectors is to split the field among a number of simple on/off detectors and infer the desired quantity from the measurement results. In this work we find an explicit analytical expression of the detection probability for any number of input photons, any number of on/off detectors, and we include quantum efficiency and a false count probability. This allows us to explicitly invert the conditional probability using Bayes’ theorem and express the number of photons that we had at the input in the most unbiased way possible with ready-to-use formulas. We conclude with some examples.

© 2018 Optical Society of America

Time-dependent photon number discrimination of InGaAs/InP avalanche photodiode single-photon detector

Yi Jian, E Wu, Xiuliang Chen, Guang Wu, and Heping Zeng
Appl. Opt. 50(1) 61-65 (2011)

Quantum detector tomography of a superconducting nanostrip photon-number-resolving detector

Mamoru Endo, Tatsuki Sonoyama, Mikihisa Matsuyama, Fumiya Okamoto, Shigehito Miki, Masahiro Yabuno, Fumihiro China, Hirotaka Terai, and Akira Furusawa
Opt. Express 29(8) 11728-11738 (2021)

Benchmarking photon number resolving detectors

Jan Provazník, Lukáš Lachman, Radim Filip, and Petr Marek
Opt. Express 28(10) 14839-14849 (2020)

Self consistent, absolute calibration technique for photon number resolving detectors

A. Avella, G. Brida, I. P. Degiovanni, M. Genovese, M. Gramegna, L. Lolli, E. Monticone, C. Portesi, M. Rajteri, M. L. Rastello, E. Taralli, P. Traina, and M. White
Opt. Express 19(23) 23249-23257 (2011)

Photon-number-resolving segmented detectors based on single-photon avalanche-photodiodes

Rajveer Nehra, Chun-Hung Chang, Qianhuan Yu, Andreas Beling, and Olivier Pfister
Opt. Express 28(3) 3660-3675 (2020)