Synchronicity for quantum non-local games

Michael Brannan, Samuel J. Harris, Ivan G. Todorov, Lyudmila Turowska

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish
Article number109738
JournalJournal of Functional Analysis
Issue number2
Early online date20 Oct 2022
Publication statusPublished - 15 Jan 2023


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