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We propose an experimental scheme for testing nonlocality of a correlated two-mode quantum state of light. We show that the correlation functions violating the Bell inequalities in the proposed experiment are equal to the joint two-mode Q function and the Wigner function. This assigns a novel operational meaning to these two quasidistribution functions in tests of quantum nonlocality and also establishes a direct relationship between two intriguing aspects of quantum mechanics: the nonlocality of entangled states and the noncommutativity of quantum observables, which underlies the nonclassical structure of the phase-space quasidistribution functions.
Banaszek et al. (Mon,) studied this question.