Testing quantum nonlocality in phase space

We propose an experimental scheme for testing nonlocality of a correlated t wo-mode quantum state of light. We show that the correlation functions viol ating the Bell inequalities in the proposed experiment are equal to the joi nt two-mode Q function and the Wigner function. This assigns a novel operat ional meaning to these two quasidistribution functions in tests of quantum nonlocality and also establishes a direct relationship between two intrigui ng aspects of quantum mechanics: the nonlocality of entangled states and th e noncommutativity of quantum observables, which underlies the nonclassical structure of the phase-space quasidistribution functions.