Synchronicity for quantum non-local games
Journal article, 2023

We introduce concurrent quantum non-local games, quantum output mirror games and concurrent classical-to-quantum non-local games, as quantum versions of synchronous non-local games, and provide tracial characterisations of their perfect strategies belonging to various correlation classes. We define *-algebras and C*-algebras of concurrent classical-to-quantum and concurrent quantum non-local games, and algebraic versions of the orthogonal rank of a graph. We show that quantum homomorphisms of quantum graphs can be viewed as entanglement assisted classical homomorphisms of the graphs, and give descriptions of the perfect quantum commuting and the perfect approximately quantum strategies for the quantum graph homomorphism game. We specialise the latter results to the case where the inputs of the game are based on a classical graph.

Graph homomorphism

Tracial C*-algebras

Non-local games

Author

Michael Brannan

University of Waterloo

Samuel J. Harris

Northern Arizona University

I. G. Todorov

Queen's University Belfast

University of Delaware

Lyudmyla Turowska

Chalmers, Mathematical Sciences, Analysis and Probability Theory

Journal of Functional Analysis

0022-1236 (ISSN) 1096-0783 (eISSN)

Vol. 284 2 109738

Subject Categories

Algebra and Logic

Geometry

Discrete Mathematics

DOI

10.1016/j.jfa.2022.109738

More information

Latest update

1/26/2023