Rounding near-optimal quantum strategies for nonlocal games to strategies using maximally entangled states

Abstract

For the classes of synchronous, binary constraint systems, and XOR nonlocal games, we show that near-optimal finitedimensional quantum strategies with arbitrary states are approximate representations of their affiliated nonlocal game algebra. We also show that finite-dimensional approximate representations of these nonlocal game algebras are close to near-optimal strategies where the players employ a maximally entangled state. As a corollary, we show that near-optimal quantum strategies are close to a near-optimal quantum strategy that uses a maximally entangled state.