Room 117

Identifying non-convexity in the sets of limited-dimension quantum correlations

C. Jebarathinam

IIT--Madras

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.

Journal Reference: Phys. Rev. A, vol. 92, 062120 (2015). journals.aps.org/pra/abstract/10.1103/PhysRevA.92.062120