Recently, Slofstra proved that the set of quantum correlations is not closed. We prove that
the set of synchronous quantum correlations is not closed, which implies his result, by giving …

We associate to each synchronous game an algebra whose representations determine if the
game has a perfect deterministic strategy, perfect quantum strategy or one of several other …

We explore the concept of a graph homomorphism through the lens of C⁎-algebras and
operator systems. We start by studying the various notions of a quantum graph …

Given a bipartite graph G, the graphical matrix space SG consists of matrices whose non-
zero entries can only be at those positions corresponding to edges in G. Tutte (J. London …

We prove a number of results to the effect that generic quantum graphs (defined via operator
systems as in the work of Duan-Severini-Winter/Weaver) have few symmetries: for a Zariski …

We define non-commutative versions of the vertex packing polytope, the theta convex body
and the fractional vertex packing polytope of a graph, and establish a quantum version of the …

We introduce classical and quantum no-signalling bicorrelations and characterise the
different types thereof in terms of states on operator system tensor products, exhibiting …

We study quantum versions of the Shannon capacity of graphs and non-commutative
graphs. We introduce the asymptotic spectrum of graphs with respect to quantum and …

We present a systematic development of inductive limits in the categories of ordered*-vector
spaces, Archimedean order unit spaces, matrix ordered spaces, operator systems and …

Non-commutative graph theory is an operator space generalization of graph theory. Well
known graph parameters such as the independence number and Lovász theta function were …