Homomorphisms of quantum hypergraphs

• URL: http://arxiv.org/abs/2311.06355v1
• Date: Fri, 10 Nov 2023 19:07:27 GMT
• Title: Homomorphisms of quantum hypergraphs
• Authors: Gage Hoefer, Ivan G. Todorov
• Abstract summary: We show that the relation of homomorphism of a given type satisfies natural analogues of the properties of a pre-order. We show that quantum hypergraph homomorphisms of local type are closely related, and in some cases identical, to the TRO equivalence of finite dimensionally acting operator spaces.
• Score: 0.3626013617212666
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We introduce quantum homomorphisms between quantum hypergraphs through the existence of perfect strategies for quantum non-local games, canonically associated with the quantum hypergraphs. We show that the relation of homomorphism of a given type satisfies natural analogues of the properties of a pre-order. We show that quantum hypergraph homomorphisms of local type are closely related, and in some cases identical, to the TRO equivalence of finite dimensionally acting operator spaces, canonically associated with the hypergraphs.

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