Quantum analogues of the Bell inequalities. The case of two spatially separated domains

One Investigates inequalities for the probabilities and mathematical expectations which follow from the postulates of the local quantum theory. It turns out that the relation between the quantum and the classical correlation matrices is expressed in terms of Grothendieck's known constant. It is also shown that the extremal quantum correlations characterize the Clifford algebra (i.e., canonical anticommutative relations).