Phase-space inequalities beyond negativities

TL;DR

This paper introduces a new set of inequalities involving phase-space distributions that can identify nonclassical states in quantum systems, even when distributions are non-negative, by linking negativities and observable correlations.

Contribution

It presents novel inequalities that detect nonclassicality beyond negativities, applicable to non-negative phase-space distributions, and relates them to correlation measurements.

Findings

Inequalities can certify nonclassicality in non-negative phase-space distributions.

Examples include squeezed states, lossy single-photon states, and coherent states.

The criteria are demonstrated to be effective through various quantum state examples.

Abstract

We derive a family of inequalities involving different phase-space distributions of a quantum state which have to be fulfilled by any classical state. The violation of these inequalities is a clear signature of nonclassicality. Our approach combines the characterization of nonclassical effects via negativities in phase-space distributions with inequality conditions usually being formulated for moments of physical observables. Importantly, the obtained criteria certify nonclassicality even when the involved phase-space distributions are non-negative. Moreover, we show how these inequalities are related to correlation measurements. The strength of the derived conditions is demonstrated by different examples, including squeezed states, lossy single-photon states, and even coherent states.