Almost synchronous correlations defined within tracial von Neumann algebras

Abstract

This thesis concerns a class of non-local games known as synchronous games. In recent work, it was discovered independently by [Vid22] and [PP22] that, for any synchronous games, any near-optimal finite dimensional strategy is always near some convex combina tions of projective strategies that employ a maximally entangled state. The main technical contribution of this thesis is a proposed proof for extending this result to a more general class of correlations known as the tracial embeddable strategies, which is a subset of the commuting operator strategies. Tracial embeddable strategies consist of the set of strategies which can be realized on the GNS representation of some tracial von Neumann algebra (A ,τ) using the state τ . In particular, we show that any near optimal tracial embeddable strategy is close to some averages of strategies that use projective measurements on tracial states, an infinite analogue of a result about maximally entangled states.