Quantum non-Gaussianity certification of photon-number-resolving detectors

TL;DR

This paper demonstrates a method to certify the quantum non-Gaussian nature of photon-number resolving detectors through experimental tests using thermal and vacuum states, enhancing the practical characterization of quantum detectors.

Contribution

It introduces a measurement protocol adapting quantum non-Gaussianity criteria for quantum measurements, enabling direct certification of detector non-Gaussianity with minimal probing states.

Findings

Successfully certified non-Gaussianity up to 7-fold coincidences

Injection of Gaussian noise can reduce measurement time

Modified protocol with thermal state speeds up certification

Abstract

We report on direct experimental certification of the quantum non-Gaussian character of a photon-number resolving detector. The certification protocol is based on an adaptation of the existing quantum non-Gaussianity criteria for quantum states to quantum measurements. In our approach, it suffices to probe the detector with a vacuum state and two different thermal states to test its quantum non-Gaussianity. The certification is experimentally demonstrated for the detector formed by a spatially multiplexed array of ten single-photon avalanche photodiodes. We confirm the quantum non-Gaussianity of POVM elements $\hat{\Pi}_m$ associated with the $m$-fold coincidence counts, up to $m=7$. The experimental ability to certify from the first principles the quantum non-Gaussian character of $\hat{\Pi}_m$ is for large $m$ limited by low probability of the measurement outcomes, especially for vacuum input state. We find that the injection of independent Gaussian background noise into the detector can be helpful and may reduce the measurement time required for reliable confirmation of quantum non-Gaussianity. In addition, we modified and experimentally verified the quantum non-Gaussianity certification protocol employing a third thermal state instead of a vacuum to speed up the whole measurement. Our findings demonstrate the existence of efficient tools for the practical characterization of fundamental non-classical properties and benchmarking of complex optical quantum detectors.