Bell Inequalities in Four Dimensional Phase Space and the Three Marginal Theorem

Details Bell Inequalities in Four Dimensional Phase Space and the Three Marginal Theorem Bell Inequalities in Four Dimensional Phase Space and the Three Marginal Theorem

2002-05-29

arxiv.org/abs/quant-ph/0205185v1

Physics

Quantum Physics

21 pages, Latex, no figures

Scientific paper

10.1063/1.1578532

We address the classical and quantum marginal problems, namely the question of simultaneous realizability through a common probability density in phase space of a given set of compatible probability distributions. We consider only distributions authorized by quantum mechanics, i.e. those corresponding to complete commuting sets of observables. For four-dimensional phase space with position variables qi and momentum variables pj, we establish the two following points: i) given four compatible probabilities for (q1,q2), (q1,p2), (p1,q2) and (p1,p2), there does not always exist a positive phase space density rho({qi},{pj}) reproducing them as marginals; this settles a long standing conjecture; it is achieved by first deriving Bell-like inequalities in phase space which have their own theoretical and experimental interest. ii) given instead at most three compatible probabilities, there always exist an associated phase space density rho({qi},{pj}); the solution is not unique and its general form is worked out. These two points constitute our ``three marginal theorem''.

Affiliated with

Also associated with

No associations

Rating

Bell Inequalities in Four Dimensional Phase Space and the Three Marginal Theorem does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Bell Inequalities in Four Dimensional Phase Space and the Three Marginal Theorem, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Bell Inequalities in Four Dimensional Phase Space and the Three Marginal Theorem will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-169520