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

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