It is shown that the applicability conditions for the inverse Bernoulli transform method to solve the inverse problem of photocount statistics are determined by the fulfillment of the associativity condition for multiplying the matrices included in this transformation. A general criterion for evaluating the photocount distributions $Q_m$ in the case of few-photon light, which makes it possible to establish whether the solution to the inverse problem of photocount statistics by the inverse Bernoulli transform method is applicable for $\eta <0.5$, is found. As an example of the application of the obtained criterion, the critical quantum efficiency ${\eta }_{\text{cr}}$ is found for compound Poisson distribution, below which the solution of the inverse problem of photocount statistics becomes incorrect. Additionally it is shown that the normalization of $Q_m$ is not sufficient to obtain a correct solution using the inverse Bernoulli transform.

• Received 3 August 2022
• Accepted 3 April 2023

DOI:https://doi.org/10.1103/PhysRevA.107.043710