PIRSA:18080036

A compositional approach to quantum functions, and the Morita theory of quantum graph isomorphisms

Verdon, D. (2018). A compositional approach to quantum functions, and the Morita theory of quantum graph isomorphisms. Perimeter Institute. https://pirsa.org/18080036

Verdon, Dominic. A compositional approach to quantum functions, and the Morita theory of quantum graph isomorphisms. Perimeter Institute, Aug. 02, 2018, https://pirsa.org/18080036 

          @misc{ pirsa_PIRSA:18080036,
            doi = {10.48660/18080036},
            url = {https://pirsa.org/18080036},
            author = {Verdon, Dominic},
            keywords = {Quantum Foundations},
            language = {en},
            title = {A compositional approach to quantum functions, and the Morita theory of quantum graph isomorphisms},
            publisher = {Perimeter Institute},
            year = {2018},
            month = {aug},
            note = {PIRSA:18080036 see, \url{https://pirsa.org}}
          }

Dominic Verdon University of Oxford

DOI 10.48660/18080036
Collection
Talk Type Conference
Subject

Abstract

Certain nonlocal games exhibiting quantum advantage, such as the quantum graph homomorphism and isomorphism games, have composable quantum strategies which are naturally interpreted as structure-preserving functions between finite sets. We propose a natural compositional framework for noncommutative finite set theory in which these quantum strategies appear naturally, and which connects nonlocal games with recent work on compact quantum groups. We apply Morita-theoretical machinery within this framework to characterise, classify, and construct quantum strategies for the graph isomorphism game. This is joint work with Benjamin Musto and David Reutter, based on the papers 1711.07945 and 1801.09705.