Speaker: Gage Hoefer, University of Delaware

Date: April 15, 2025

Abstract: A non-local game is one in which two players cooperatively try to convince a third party that they possess a piece of information, which they may or may not legitimately have. The study of non-local games- rooted in Bell’s celebrated work from the ‘60’s- has grown significantly over the past few decades, due to their use in showing the benefits and limitations of quantum entanglement. In this talk, I will provide a brief summary of non-local game theory, including different types of strategies available to the players, emphasizing quantum strategies (which arise from shared entangled resources between the two). We show how strategies for non-local games can be characterized by states acting on tensor products of canonical operator systems, indicating connections between the study of operator algebras and non-local games. Utilizing the simulation paradigm in information theory, we introduce notions of quantum homomorphisms and quantum isomorphisms of non-local games, dependent on different no-signalling correlation classes. Using an operator system approach, we investigate game strategy transfer, and how game homomorphisms affect optimal game values. Time permitting, we also discuss how we may lift these results to the setting of quantum games, in which we replace questions and answers from finite sets with quantum states as inputs and outputs.

This talk will be partially based on joint work with Ivan G. Todorov, along with recent solo work.