Nonclassical correlations of radiation in relation to Bell nonlocality

TL;DR

This paper explores nonclassical correlations in quantum radiation, demonstrating their relation to Bell nonlocality, and introduces a modified Bell inequality applicable to continuous variables, supported by analysis of specific quantum states.

Contribution

It establishes a link between nonclassical correlations and Bell nonlocality, proposing a new Bell inequality formulation for continuous variables.

Findings

Nonclassical correlations cannot be simulated by classical mixtures.

Modified Bell inequalities can test nonclassical correlations in continuous variables.

Analysis of two-mode squeezed and hybrid entangled states supports the theoretical framework.

Abstract

We analyze nonclassical correlations between outcomes of measurements conducted on two spatial radiation modes. These correlations cannot be simulated with statistical mixtures of coherent states or, more generally, with non-negative phase-space functions of quantum states and measurements. We argue that nonclassical correlations are naturally related to Bell nonlocality, the former being a more general class of quantum correlations. Indeed, it is known that local realistic as well as noncontextual models correspond to non-negative solutions to a system of linear equations for the joint probability distributions of all observables. We demonstrate that nonclassical correlations correspond to a particular solution to this system, which may have negative values even if local realism is not violated. A modification of Bell inequalities enables us to test such correlations. At the same time, our approach leads to a formulation of Bell inequalities applicable also to continuous variables. The results are illustrated with two-mode squeezed vacuum states and with hybrid entangled states (Schr\"odinger-Cat states), one mode being analyzed by balanced and the other one by unbalanced homodyne detection.