Parallel Repetition of Entangled Games

TL;DR

This paper demonstrates that parallel repetition can effectively reduce the maximum winning probability in entangled games, extending classical results to the quantum entangled setting with new techniques.

Contribution

It proves for the first time that parallel repetition decreases success probability in entangled games, introducing an orthogonalization lemma for operators.

Findings

Success probability decreases with parallel repetition in entangled games

Extension of classical parallel repetition results to quantum entangled settings

Introduction of an orthogonalization lemma for operators

Abstract

We consider one-round games between a classical referee and two players. One of the main questions in this area is the parallel repetition question: Is there a way to decrease the maximum winning probability of a game without increasing the number of rounds or the number of players? Classically, efforts to resolve this question, open for many years, have culminated in Raz's celebrated parallel repetition theorem on one hand, and in efficient product testers for PCPs on the other. In the case where players share entanglement, the only previously known results are for special cases of games, and are based on techniques that seem inherently limited. Here we show for the first time that the maximum success probability of entangled games can be reduced through parallel repetition, provided it was not initially 1. Our proof is inspired by a seminal result of Feige and Kilian in the context of classical two-prover one-round interactive proofs. One of the main components in our proof is an orthogonalization lemma for operators, which might be of independent interest.