Anchored parallel repetition for nonlocal games

Mohammad Bavarian; Thomas Vidick; Henry Yuen

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arXiv · 1509.07466

Anchored parallel repetition for nonlocal games

Mohammad Bavarian·Thomas Vidick·Henry Yuen

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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.

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Mohammad Bavarian, Thomas Vidick, Henry Yuen. 2015-09-24. Anchored parallel repetition for nonlocal games. https://arxiv.org/abs/1509.07466

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