We introduce the (G, H)-isomorphism game, a new two-player non-local game that classical
players can win with certainty iff the graphs G and H are isomorphic. We then define …

We study the graph isomorphism game that arises in quantum information theory. We prove
that the non-commutative algebraic notion of a quantum isomorphism between two graphs is …

We introduce a notion of quantum function and develop a compositional framework for finite
quantum set theory based on a 2-category of quantum sets and quantum functions. We use …

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 undertake a study of the notion of a quantum graph over arbitrary finite-dimensional $
C^* $-algebras $ B $ equipped with arbitrary faithful states. Quantum graphs are realised …

We describe the main classes of non-signalling bipartite correlations in terms of states on
operator system tensor products. This leads to the introduction of another new class of …

We introduce a new class of non-local games and corresponding densities, which we call
bisynchronous. Bisynchronous games are a subclass of synchronous games and exhibit …

Mathematical models of quantum mechanics can be studied and distinguished using
nonlocal games. We discuss a class of nonlocal games called synchronous linear constraint …

We introduce and examine three subclasses of the family of quantum no-signalling (QNS)
correlations introduced by Duan and Winter: quantum commuting, quantum and local. We …

The “noncommutative graphs” which arise in quantum error correction are a special case of
the quantum relations introduced in Weaver (Quantum relations. Mem Am Math Soc 215 (v …