Antonios Varvitsiotis

On the minimum dimension of a Hilbert space needed to generate a quantum correlation

Consider a two-party correlation that can be generated by performing local measurements on a bipartite quantum system. A question of fundamental importance is to understand how many resources, which we quantify by the dimension of the underlying quantum system, are needed to reproduce this correlation. In this Letter, we identify an easy-to-compute lower bound on the smallest Hilbert space dimension needed to generate a given two-party quantum correlation. We show that our bound is tight on many well-known correlations and discuss how it can rule out correlations of having a finite-dimensional quantum representation. We show that our bound is multiplicative under product correlations and also that it can witness the nonconvexity of certain restricted-dimensional quantum correlations.

Completely positive semidefinite rank

An

Graph Cores via Universal Completability

n\times n

Quantum and non-signalling graph isomorphisms

n×n matrix X is called completely positive semidefinite (cpsd) if there exist

On deciding the existence of perfect entangled strategies for nonlocal games.

d\times d

Structure of the set of quantum correlators via semidefinite programming

d×d Hermitian positive semidefinite matrices