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We consider quantum XOR games, defined in [11], from the perspective ofunitary correlations defined in [7]. We show that Connes' embedding problem hasa positive answer if and only if every quantum XOR game has entanglement biasequal to the commuting bias. In particular, the embedding problem is equivalentto determining whether every quantum XOR game $G$ with a winning strategy inthe commuting model also has a winning strategy in the approximatefinite-dimensional model.

Connes' Embedding Problem and Winning Strategies for Quantum XOR Games