Synchronicity for quantum non-local games
- URL: http://arxiv.org/abs/2106.11489v1
- Date: Tue, 22 Jun 2021 02:40:41 GMT
- Title: Synchronicity for quantum non-local games
- Authors: Michael Brannan, Samuel J. Harris, Ivan G. Todorov, Lyudmila Turowska
- Abstract summary: We show that quantum homomorphisms of quantum graphs can be viewed as entanglement assisted classical homomorphisms of the graphs.
We give descriptions of the perfect quantum commuting and the perfect approximately quantum strategies for the quantum graph homomorphism game.
- Score: 0.7646713951724009
- License: http://creativecommons.org/licenses/by/4.0/
- 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.
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