Quantum α-entropy inequalities: independent condition for local realism?

Abstract

Quantum α-entropy inequalities equivalent to Bell's inequality for pure states are considered in the context of the local hidden variable (LHV) model and compared with Bell's inequalities. For α = 1,2 they are shown to be satisfied by convex combinations of product states and Werner's mixtures admitting the model. The 2-entropy inequality is proven to be stronger than Bell's inequality in the two-spin- 1 2 case. In the latter, the α-entropy inequalities taken as a joint condition exclude teleportation admitted in spite of the existence of the LHV model for the Werner-Popescu states.