Arbitrary violation of the Tsirelson bound

Abstract

We present a simple hidden variable model for the singlet state of a pair of qubits, characterized by two kinds, hierarchically ordered, of hidden variables. We prove that, averaging over both types of variables, one reproduces all the quantum mechanical correlations of the singlet state. On the other hand, averaging only over the hidden variables of the lower level, one obtains a general formal theoretical scheme exhibiting correlations stronger than the quantum ones, but with faster-than-light communication forbidden. This result is interesting by itself since it shows that a violation of the quantum bound for nonlocal correlations can be implemented in a precise physical manner and not only mathematically, and it suggests that resorting to two levels of nonlocal hidden variables might led to a deeper understanding of the physical principles at the basis of quantum nonlocality.