Extended nonlocal games and monogamy-of-entanglement games

TL;DR

This paper introduces extended nonlocal games where players share a tripartite quantum state and the winning conditions depend on measurements by a referee, extending previous monogamy-of-entanglement game concepts.

Contribution

It generalizes nonlocal and monogamy-of-entanglement games, proving hierarchy convergence and extending key results in the field.

Findings

Hierarchy of semidefinite programs converges to optimal value

Extended monogamy-of-entanglement games analyzed

New bounds and properties established for these games

Abstract

We study a generalization of nonlocal games---which we call extended nonlocal games---in which the players, Alice and Bob, initially share a tripartite quantum 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 randomly selected questions. Our study of this class of games was inspired by the monogamy-of-entanglement games introduced by Tomamichel, Fehr, Kaniewski, and Wehner, which they also generalize. We prove that a natural extension of the Navascues--Pironio--Acin hierarchy of semidefinite programs converges to the optimal commuting operator value of extended nonlocal games, and we prove two extensions of results of Tomamichel et al. concerning monogamy-of-entanglement games.