Continuous variable Bell inequalities - Peter Marzlin

Bell inequalities are relations that are fulfilled for very general classes of classical systems but are violated in quantum mechanics. They provide an upper bound for the mean value of observables which is based on only a few basic assumptions. Most Bell inequalities have been derived for observables with dichotomic spectra. We present an approach to construct Bell inequalities for continuous variable systems which employs the Moyal-Weyl representation of quantum mechanics in phase space and quantum conditional probabilities. An example of a Bell inequality violation that utilizes the non-positivity of the Wigner function is presented.