Parallel Repetition for the GHZ Game: Exponential Decay

TL;DR

This paper proves that the success probability of the repeated GHZ game decreases exponentially with the number of repetitions, using techniques from additive combinatorics to improve previous bounds.

Contribution

It introduces a novel exponential decay bound for the repeated GHZ game, surpassing prior polynomial bounds, through a reduction to approximate subgroup problems.

Findings

Success probability decays exponentially with repetitions

Improved bound from polynomial to exponential decay

Reduction to additive combinatorics problems

Abstract

We show that the value of the $n$-fold repeated GHZ game is at most $2^{-\Omega(n)}$, improving upon the polynomial bound established by Holmgren and Raz. Our result is established via a reduction to approximate subgroup type questions from additive combinatorics.