Quantum Games and Synchronicity

• URL: http://arxiv.org/abs/2408.15444v1
• Date: Tue, 27 Aug 2024 23:27:59 GMT
• Title: Quantum Games and Synchronicity
• Authors: Adina Goldberg,
• Abstract summary: We extend nonlocal games to allow quantum questions and answers. Equations are presented using a diagrammatic calculus for tensor categories. We extend the standard definitions, including strategies, correlations, and synchronicity.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: In the flavour of categorical quantum mechanics, we extend nonlocal games to allow quantum questions and answers, using quantum sets (special symmetric dagger Frobenius algebras) and the quantum functions of arXiv:1711.07945. Equations are presented using a diagrammatic calculus for tensor categories. To this quantum question and answer setting, we extend the standard definitions, including strategies, correlations, and synchronicity, and we use these definitions to extend results about synchronicity. We extend the graph homomorphism (isomorphism) game to quantum graphs, and show it is synchronous (bisynchronous) and that its perfect quantum-commuting (bi)strategies are quantum graph homomorphisms (isomorphisms). Our extended definitions agree with the existing quantum games literature, except in the case of synchronicity.

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