Entanglement versus Bell Violations and Their Behavior under Local Filtering Operations

Frank Verstraete and Michael M. Wolf

Phys. Rev. Lett. 89, 170401 – Published 2 October 2002

Abstract

We discuss the relations between the violation of the Clauser-Horne-Shimony-Holt (CHSH) Bell inequality for systems of two qubits on the one side and entanglement of formation, local filtering operations, and the entropy and purity on the other. We calculate the extremal Bell violations for a given amount of entanglement of formation and characterize the respective states, which turn out to have extremal properties also with respect to the entropy, purity, and several entanglement monotones. The optimal local filtering operations leading to the maximal Bell violation for a given state are provided, and the special role of the resulting Bell diagonal states in the context of Bell inequalities is discussed.

Received 13 December 2001

DOI:https://doi.org/10.1103/PhysRevLett.89.170401

Authors & Affiliations

Frank Verstraete^*

Department of Mathematical Physics and Astronomy, Ghent University, Ghent, Belgium
Department of Electrical Engineering (SISTA), KU Leuven, Leuven, Belgium

Michael M. Wolf^†