Extended Nonlocal Games

TL;DR

This paper introduces and explores extended nonlocal games, a broader class of quantum games involving a shared tripartite state with a referee, enhancing understanding of entanglement and nonlocality in quantum information theory.

Contribution

It develops a formal framework for extended nonlocal games and analyzes their properties, extending the traditional nonlocal game model to include referee-involved measurement outcomes.

Findings

Extended nonlocal games generalize standard nonlocal games.

The framework links properties of extended games to quantum entanglement.

Insights into how referee measurements influence game outcomes.

Abstract

The notions of entanglement and nonlocality are among the most striking ingredients found in quantum information theory. One tool to better understand these notions is the model of nonlocal games; a mathematical framework that abstractly models a physical system. The simplest instance of a nonlocal game involves two players, Alice and Bob, who are not allowed to communicate with each other once the game has started and who play cooperatively against an adversary referred to as the referee. The focus of this thesis is a class of games called extended nonlocal games, of which nonlocal games are a subset. In an extended nonlocal game, the players initially share a tripartite state with the referee. In such games, the winning conditions for Alice and Bob may depend on outcomes of measurements made by the referee, on its part of the shared quantum state, in addition to Alice and Bob's answers to the questions sent by the referee. We build up the framework for extended nonlocal games and study their properties and how they relate to nonlocal games.