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