Abstract

Consider nonlocal games, but allow for quantum questions and answers. We call these objects quantum games. It turns out the typical definitions from the nonlocal games literature can be extended and many of the typical results still hold in this quantum setting. The analogies to the typical setting can be seen clearly using string diagrams! This talk contains many diagrams. We use string diagrams to introduce extended definitions of games, correlations, and synchronicity. We show that perfect correlations and strategies for synchronous quantum games must be synchronous. Time permitting, as a key example: When the graph homomorphism game is extended to quantum graphs, we get a synchronous game, whose perfect strategies are quantum graph homomorphisms! The talk is based on a preprint Quantum games and synchronicity. This work is inspired by Musto, Reutter, and Verdon’s paper A compositional approach to quantum functions, and relies heavily on the reference Categories for Quantum Theory by Heunen and Vicary for string diagrams in quantum information.