Towards Additivity of Entanglement of Formation

Abstract

Quantum entanglement is the most precious and most un- usual quantum computation and communication resource. It is therefore of importance to understand how much of entanglement particular quan- tum states have, and what are the laws and limitations of transformation of entanglement from one form to another. To deal with this problem, it is necessary to use proper measures of entanglement that have nice prop- erties. One of the most natural of such measures is that of entanglement of formation, and one of the major and long standing open problems con- cerning that measure is whether it is additive. In this paper we attack this hard problem. We show that for an important special case of states entangled formation is indeed additive. We also discuss this additivity problem and its merit in a broader context.