Nonclassicality detection from few Fock-state probabilities

TL;DR

This paper introduces new criteria for detecting nonclassicality in photon and phonon statistics that are more robust and complete than previous methods, applicable with limited Fock-state probability data in various experimental setups.

Contribution

The authors develop a new set of criteria that extend Klyshko's criteria, providing a more complete and experimentally feasible method for nonclassicality detection from limited Fock-state probabilities.

Findings

The criteria detect all incompatible finite distributions with classical states when few probabilities are known.

They identify nonclassical states even in noisy conditions where Klyshko's criteria fail.

The method is applicable to diverse quantum systems like trapped ions, superconducting circuits, and optical experiments.

Abstract

We devise a new class of criteria to certify the nonclassicality of photon- and phonon-number statistics. Our criteria extend and strengthen the broadly used Klyshko's criteria, which require knowledge of only a finite set of Fock-state probabilities. This makes the criteria well-suited to experimental implementation in realistic conditions. Moreover, we prove the completeness of our method in some scenarios, showing that, when only two or three Fock-state probabilities are known, it detects all finite distributions incompatible with classical states. In particular, we show that our criteria detect a broad class of noisy Fock states as nonclassical, even when Klyshko's do not. The method is directly applicable to trapped-ion, superconducting circuits, and optical and optomechanical experiments with photon-number resolving detectors. This work represents a significant milestone towards a complete characterisation of the nonclassicality accessible from limited knowledge of the Fock-state probabilities.