Embezzlement of entanglement was studied by van Dam and Hayden who showed that it was imposible to catylyically produce entanglement in the tensor product model, but that one could "nearly" acheive this goal. However, in the commuting operator model one can accomplish this task. We show that there is a parallel between this theory and Tsirelson's problems about the different models for conditional probability densities. In analogy there is a theory of "unitary correlations" that yields a set of matrices that allows one to study quantum input--classical output games.