Identifying nonconvexity in the sets of limiteddimension quantum correlations
Abstract
Quantum theory is known to be nonlocal in the sense that separated parties can perform measurements on a shared quantum state to obtain correlated probability distributions, which cannot be achieved if the parties share only classical randomness. Here we find that the set of distributions compatible with sharing quantum states subject to some sufficiently restricted dimension is neither convex nor a superset of the classical distributions. We examine the relationship between quantum distributions associated with a dimensional constraint and classical distributions associated with limited shared randomness. We prove that quantum correlations are convex for certain finite dimension in certain Bell scenarios and that they sometimes offer a dimensional advantage in realizing local distributions. We also consider if there exist Bell scenarios where the set of quantum correlations is never convex with finite dimensionality.
 Publication:

Physical Review A
 Pub Date:
 December 2015
 DOI:
 10.1103/PhysRevA.92.062120
 arXiv:
 arXiv:1506.01119
 Bibcode:
 2015PhRvA..92f2120D
 Keywords:

 03.65.Ud;
 03.65.Aa;
 03.65.Ta;
 Entanglement and quantum nonlocality;
 Foundations of quantum mechanics;
 measurement theory;
 Quantum Physics
 EPrint:
 v3 was been updated so that the arXiv version matches the published version's content. v4 corrects small remaining typos, corrects footnote #3 which references arXiv:1507.00213, and restores the supplementary Mathematica notebook to the arXiv source