Statistical Inference from Imperfect Photon Detection

TL;DR

This paper develops a statistically sound method for inferring quantum state outcome probabilities from photon detection data, accounting for detector imperfections like dark counts and inefficiencies, applicable to various measurement setups.

Contribution

It introduces a new statistical inference approach for photon detection data with imperfect detectors in quantum tomography, enhancing accuracy in outcome probability estimation.

Findings

Provides a method for accurate probability inference with imperfect detectors

Applicable to both pulsed and continuous wave photon measurements

Improves quantum state reconstruction reliability

Abstract

We consider the statistical properties of photon detection with imperfect detectors that exhibit dark counts and less than unit efficiency, in the context of tomographic reconstruction. In this context, the detectors are used to implement certain POVMs that would allow to reconstruct the quantum state or quantum process under consideration. Here we look at the intermediate step of inferring outcome probabilities from measured outcome frequencies, and show how this inference can be performed in a statistically sound way in the presence of detector imperfections. Merging outcome probabilities for different sets of POVMs into a consistent quantum state picture has been treated elsewhere [K.M.R. Audenaert and S. Scheel, New J. Phys. 11, 023028 (2009)]. Single-photon pulsed measurements as well as continuous wave measurements are covered.