Almost synchronous correlations defined within tracial von Neumann algebras
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Date
2022-08-24
Authors
Lin, Junqiao
Journal Title
Journal ISSN
Volume Title
Publisher
University of Waterloo
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.
Description
Keywords
quantum computing, non-local games