Reducing the number of inputs in nonlocal games

Abstract

In this work we show how a vector-valued version of Schechtman's empirical method can be used to reduce the number of inputs in a nonlocal game $G$ while preserving the quotient ${\beta }^{\ast }(G)/\beta (G)$ of the quantum over the classical bias. We apply our method to the Khot-Vishnoi game, with exponentially many questions per player, to produce another game with polynomially many ($N\approx n^8$) questions so that the quantum over the classical bias is $\Omega (n/{\log }^{2}n)$.

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