Proposal for a macroscopic test of local realism with phase-space measurements

摘要

We propose a new test of local realism based on correlation measurements ofcontinuum valued functions of positions and momenta, known as modularvariables. The Wigner representation of these observables are bounded in phasespace, and therefore, the associated inequality holds for any state describedby a non-negative Wigner function. This agrees with Bell's remark that positiveWigner functions, serving as a valid probability distribution over local(hidden) phase space coordinates, do not reveal non-locality. We construct aclass of entangled states resulting in a violation of the inequality, and thustruly demonstrate non-locality in phase space. The states can be realizedthrough grating techniques in space-like separated interferometric setups. Thenon-locality is verified from the spatial correlation data, collected from thescreens.