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.

21 pages, 5 figures

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Cited by in corpus (6)

• Photon-number resolution with microwave Josephson photomultipliers
• Tight inequalities for nonclassicality of measurement statistics
• Nonclassical correlations of radiation in relation to Bell nonlocality
• Time correlations in atmospheric quantum channels
• Nonclassical photocounting statistics with a single on-off detector
• Latent optical nonclassicality of conditionally prepared states