Quantum Computation and Information Seminar 

03/12/2004, 15:00 — 16:00 — Room P4.35, Mathematics Building
Adán Cabello, University of Seville

How much larger than classical correlations are quantum correlations?

It is commonly stated that quantum correlations are "larger" than classical ones. This statement, which has been described as "the most profound discovery of science," is based on the fact that some predictions of quantum mechanics violate Bell's inequalities, derived from some assumptions of classical physics. However, the question of how much larger than classical correlations are quantum correlations did not have a precise answer beyond the fact that quantum mechanics violates the CHSH-Bell inequality up to $2\sqrt{2}$ (Tsirelson's bound), while the classical bound is just 2. We shall show that the volume of the set of quantum correlations is $(3\pi /8{)}^2=1.388$ larger than the volume of the set of correlations obtainable by classical deterministic theories, but is only $3{\pi }^2/32=0.925$ of the volume allowed by probabilistic theories. We use these results to quantify the success of some approximate characterizations of the set of quantum correlations using linear and quadratic inequalities.

Are larger-than-quantum correlations possible? The quantum correlations appearing in the CHSH-Bell inequality can give values between the classical bound and Tsirelson's bound. However, for a given set of local observables, there are values in this range that are unattainable by any quantum state. We provide the analytical expression for the attainable values and the corresponding bound. We also describe how to experimentally trace this bound. Two groups have recently performed experiments to trace this bound, confirming the predictions of quantum mechanics and finding no evidence of larger-than-quantum correlations.