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

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.