Tomography of a single-atom-resolved detector in the presence of shot-to-shot number fluctuations

Tomography of single-particle-resolved detectors is of primary importance for characterizing particle correlations with applications in quantum metrology, quantum simulation and quantum computing. However, it is a non-trivial task in practice due to the unavoidable presence of noise that affects the measurement but does not originate from the detector. In this work, we address this problem for a three-dimensional single-atom-resolved detector where shot-to-shot atom number fluctuations are a central issue to perform a quantum detector tomography. We overcome this difficulty by exploiting the parallel measurement of counting statistics in sub-volumes of the detector, from which we evaluate the effect of shot-to-shot fluctuations and perform a local tomography of the detector. In addition, we illustrate the validity of our method from applying it to Gaussian quantum states with different number statistics. Finally, we show that the response of Micro-Channel Plate detectors is well-described from using a binomial distribution with the detection efficiency as a single parameter.