Quantum non-Gaussianity criteria based on vacuum probabilities of original and attenuated state

TL;DR

This paper develops practical criteria for certifying quantum non-Gaussian states using vacuum probabilities, applicable to multimode states and requiring only a single photodetector, thus simplifying experimental procedures.

Contribution

It introduces new criteria for quantum non-Gaussianity detection based on vacuum probabilities, applicable to arbitrary multimode states and compatible with simple detection setups.

Findings

Criteria successfully detect non-Gaussianity in realistic imperfect single-photon states.

The approach simplifies experimental detection by using only one photodetector.

The criteria are applicable to broadband sources and single-photon detectors.

Abstract

Quantum non-Gaussian states represent an important class of highly non-classical states whose preparation requires quantum operations or measurements beyond the class of Gaussian operations and statistical mixing. Here we derive criteria for certification of quantum non-Gaussianity based on probability of vacuum in the original quantum state and a state transmitted through a lossy channel with transmittance T. We prove that the criteria hold for arbitrary multimode states, which is important for their applicability in experiments with broadband sources and single-photon detectors. Interestingly, our approach allows to detect quantum non-Gaussianity using only one photodetector instead of complex multiplexed photon detection schemes, at the cost of increased experimental time. We also formulate a quantum non-Gaussianity criterion based on the vacuum probability and mean photon number of the state and we show that this criterion is closely related to the criteria based on pair of vacuum probabilities. We illustrate the performance of the obtained criteria on the example of realistic imperfect single-photon states modeled as a mixture of vacuum and single-photon states with background Poissonian noise.