Synchronicity for quantum non-local games
Abstract
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.
Keywords
Cite
@article{arxiv.2106.11489,
title = {Synchronicity for quantum non-local games},
author = {Michael Brannan and Samuel J. Harris and Ivan G. Todorov and Lyudmila Turowska},
journal= {arXiv preprint arXiv:2106.11489},
year = {2021}
}