Testing nonclassicality and non-Gaussianity in phase space

TL;DR

This paper introduces a phase-space test for nonclassicality and non-Gaussianity of quantum states, demonstrating its effectiveness both theoretically and experimentally, and providing a new criterion for genuine quantum non-Gaussian states.

Contribution

It proposes a novel phase-space nonclassicality test analogous to nonlocality tests, capable of detecting all pure nonclassical Gaussian states and identifying genuine quantum non-Gaussianity.

Findings

Successfully demonstrated the test experimentally.

Detected quantum non-Gaussianity by phase-space point selection.

Established bounds for Gaussian states and their mixtures.

Abstract

We theoretically propose and experimentally demonstrate a nonclassicality test of single-mode field in phase space, which has an analogy with the nonlocality test proposed by Banaszek and Wodkiewicz [Phys. Rev. Lett. 82, 2009 (1999)]. Our approach to deriving the classical bound draws on the fact that the Wigner function of a coherent state is a product of two independent distributions as if the orthogonal quadratures (position and momentum) in phase space behave as local realistic variables. Our method detects every pure nonclassical Gaussian state, which can also be extended to mixed states. Furthermore, it sets a bound for all Gaussian states and their mixtures, thereby providing a criterion to detect a genuine quantum non-Gaussian state. Remarkably, our phase-space approach with invariance under Gaussian unitary operations leads to an optimized test for a given non-Gaussian state. We experimentally show how this enhanced method can manifest quantum non-Gaussianity of a state by simply choosing phase-space points appropriately, which is essentially equivalent to implementing a squeezing operation on a given state.