Demonstrating nonclassicality and non-Gaussianity of single-mode fields: Bell-type tests using generalized phase-space distributions

TL;DR

This paper introduces Bell-type tests using generalized phase-space distributions to detect nonclassicality and non-Gaussianity in single-mode fields, enhancing detection capabilities and linking to nonlocality testing.

Contribution

It develops new Bell-type criteria based on phase-space points to identify nonclassical and non-Gaussian states, including optimization via squeezing transformations.

Findings

Detects all pure nonclassical Gaussian states

Sets bounds for Gaussian states and mixtures

Enables nonlocality resource identification

Abstract

We present Bell-type tests of nonclassicality and non-Gaussianity for single-mode fields employing a generalized quasiprobability function. Our nonclassicality tests are based on the observation that two orthogonal quadratures in phase space (position and momentum) behave as independent realistic variables for a coherent state. Taking four (three) points at the vertices of a rectangle (right triangle) in phase space, our tests detect every pure nonclassical Gaussian state and a range of mixed Gaussian states. These tests also set an upper bound for all Gaussian states and their mixtures, which thereby provide criteria for genuine quantum non-Gaussianity. We optimize the non-Gaussianity tests by employing a squeezing transformation in phase space that converts a rectangle (right triangle) to a parallelogram (triangle), which enlarges the set of non-Gaussian states detectable in our formulation. We address fundamental and practical limits of our generalized phase-space tests by looking into their relation with decoherence under a lossy Gaussian channel and their robustness against finite data and nonoptimal choice of phase-space points. Furthermore, we demonstrate that our parallelogram test can identify useful resources for nonlocality testing in phase space.