Dual form of the phase-space classical simulation problem in quantum optics

TL;DR

This paper establishes a dual framework linking phase-space classical simulation impossibility to quantum nonclassicality, using Bell inequality analogues to identify nonclassical states in quantum optics.

Contribution

It introduces a dual formulation of phase-space classical simulation problems, providing a new criterion for nonclassicality based on Bell inequality analogues.

Findings

Violations of the Bell-like inequalities indicate nonclassical states.

The method applies to various optical measurements including photocounting and homodyne detection.

The approach unifies the understanding of nonclassicality in phase-space representations.

Abstract

In quantum optics, nonclassicality of quantum states is commonly associated with negativities of phase-space quasiprobability distributions. We argue that the impossibility of any classical simulations with phase-space functions is a necessary and sufficient condition of nonclassicality. The problem of such phase-space classical simulations for particular measurement schemes is analysed in the framework of Einstein-Podolsky-Rosen-Bell's principles of physical reality. The dual form of this problem results in an analogue of Bell inequalities. Their violations imply the impossibility of phase-space classical simulations and, as a consequence, nonclassicality of quantum states. We apply this technique to emblematic optical measurements such as photocounting, including the cases of realistic photon-number resolution and homodyne detection in unbalanced, balanced, and eight-port configurations.