A parallel repetition theorem for all entangled games

TL;DR

This paper proves a general parallel repetition theorem for all entangled two-player games, showing that their entangled value diminishes polynomially with repetitions, which was previously unknown for general cases.

Contribution

It establishes the first general parallel repetition bound for all entangled games, extending quantum analogues beyond special classes.

Findings

Entangled value decreases at least as fast as n^{-1/4} log n with repetitions.

First proof that entangled value converges to zero for all games with initial value less than 1.

Uses a novel combination of classical and quantum correlated sampling techniques.

Abstract

The behavior of games repeated in parallel, when played with quantumly entangled players, has received much attention in recent years. Quantum analogues of Raz's classical parallel repetition theorem have been proved for many special classes of games. However, for general entangled games no parallel repetition theorem was known. We prove that the entangled value of a two-player game $G$ repeated $n$ times in parallel is at most $c_G n^{-1/4} \log n$ for a constant $c_G$ depending on $G$, provided that the entangled value of $G$ is less than 1. In particular, this gives the first proof that the entangled value of a parallel repeated game must converge to 0 for all games whose entangled value is less than 1. Central to our proof is a combination of both classical and quantum correlated sampling.