Journal of Operator Theory

Volume 96, Issue 1, Summer 2026 pp. 171-183.

Almost synchronous correlations and Tomita-Takesaki theory

Authors: Amine Marrakchi (1), Mikael De La Salle (2)
Author institution: (1) UMPA, ENSL, CNRS, Lyon, 69364, France
(2) Université Lyon 1, CNRS, Villeurbanne, 69622, France

Summary: The aim of this note is to present a ``type III'' generalization of a distribution lemma of Connes. We then derive, following Vidick, consequences on infinite-dimensional quantum strategies for non-local games.

DOI: http://dx.doi.org/10.7900/jot.2025jan29.2507
Keywords: von Neumann algebras, Tomita-Takesaki theory, quantum games, non-local games, quantum correlations, non-commutative $L_p$-spaces

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