Anchored parallel repetition for nonlocal games

TL;DR

This paper introduces an anchoring transformation for nonlocal games that enables exponential decay in quantum value under parallel repetition, advancing gap amplification techniques in quantum information theory.

Contribution

The authors develop a new anchoring transformation for nonlocal games that achieves exponential decay of quantum value, providing the first such gap amplification method for general two-player nonlocal games.

Findings

Proves exponential decay of quantum value for anchored games.

Shows the transformation preserves perfect quantum value.

Provides a new technique for gap amplification in quantum nonlocal games.

Abstract

We introduce a simple transformation on two-player nonlocal games, called "anchoring", and prove an exponential-decay parallel repetition theorem for all anchored games in the setting of quantum entangled players. This transformation is inspired in part by the Feige-Kilian transformation (SICOMP 2000), and has the property that if the quantum value of the original game $G$ is $v$ then the quantum value of the anchored game $G_\bot$ is $1 - (1 - \alpha)^2 \cdot (1 - v)$ where $\alpha$ is a parameter of the transformation. In particular the anchored game has quantum value $1$ if and only if the original game $G$ has quantum value $1$. This provides the first gap amplification technique for general two-player nonlocal games that achieves exponential decay of the quantum value.