Worst case analysis of non-local games

TL;DR

This paper investigates the worst-case scenario in non-local games, where the referee's input distribution is unknown, providing insights into quantum versus classical strategies without relying on probabilistic assumptions.

Contribution

It introduces the analysis of non-local games under worst-case conditions, expanding understanding beyond traditional probabilistic frameworks.

Findings

Established bounds for non-local game performance in worst-case scenarios

Compared classical and quantum strategies in this new setting

Provided foundational results for future research in worst-case non-local games

Abstract

Non-local games are studied in quantum information because they provide a simple way for proving the difference between the classical world and the quantum world. A non-local game is a cooperative game played by 2 or more players against a referee. The players cannot communicate but may share common random bits or a common quantum state. A referee sends an input $x_i$ to the $i^{th}$ player who then responds by sending an answer $a_i$ to the referee. The players win if the answers $a_i$ satisfy a condition that may depend on the inputs $x_i$. Typically, non-local games are studied in a framework where the referee picks the inputs from a known probability distribution. We initiate the study of non-local games in a worst-case scenario when the referee's probability distribution is unknown and study several non-local games in this scenario.