Limits for entanglement measures

Michal Horodecki, Pawel Horodecki, Ryszard Horodecki

Published 1999-08-19, updated 2000-03-01Version 2

We show that {\it any} entanglement measure $E$ suitable for the regime of high number of entangled pairs satisfies $E_D\leq E\leq E_F$ where $E_D$ and $E_F$ are entanglement of distillation and formation respectively. We also exhibit a general theorem on bounds for distillable entanglement. The results are obtained by use of a very transparent reasoning based on the fundamental principle of entanglement theory saying that entanglement cannot increase under local operations and classical communication.