The Measurement and Analysis of Photon Counting Distributions

Jorge C. S. Castro, H. M. Salgado

A statistical model linking the probability of detecting photons in a photon counting experiment to the average number of input photons is used to analytically derive an error distribution of the estimates of the average number of photons in coherent input pulses. The estimates distribution determines the required number of experimental count runs required for an acceptable measurement error, for any value of the average number of input photons. An expression for the minimum detectable power by photon counting is obtained, fully capturing the effect of the photon counting statistics thereby completing an earlier analysis.

L. Basano, Pasquale Ottonello

In the measurement of triggered photon-counting distributions (TPCDs) the triggering pulse which starts a collecting interval may be picked up according to different random procedures. We investigate, both theoretically and experimentally, the extent to which TPCDs are affected by the choice of the triggering pulses. It turns out that in ordinary conditions the measured distribution may be significantly influenced by the triggering procedure. This result is another manifestation of the bunching effect and indicates that a great deal of attention should be exercised in performing and interpreting triggered photon-counting.

J. Lyons, GORDON J. TROUP

Boyu Zhou, Boulat A. Bash, Saikat Guha +1 more

We address the problem of estimating the transmissivity of the pure-loss single-mode bosonic channel from the Bayesian point of view, i.e., when a prior probability distribution function (PDF) on the transmissivity is available. We compute the quantum limit of the Bayesian minimum mean square error of estimating transmissivity. Specifically, we consider two prior PDFs: the two-point distribution (relevant for reading from an optical drive) and the beta distribution (relevant for imaging a reflective pixelated scene). If the probe's mean photon number is an integer, for the two-point PDF we prove that the optimal probe is a Fock state and the optimal measurement is photon counting, while for the beta PDF our numerical results provide evidence on the optimality of the Fock state probe and photon counting. When the probe's mean photon number is any (nonnegative) real number, we conjecture the form of the optimal probe state and we study the performance of photon counting, which is a suboptimal yet practical measurement. Our methods can be applied for any prior PDF. We discuss how different precision metrics and priors on the parameter influence the quantum-optimal probe and measurement. To our knowledge, these results on transmissivity estimation with quantum-limited precision represent the first Bayesian analysis of the problem.