REE From EOF

TL;DR

This paper explores the relationship between entanglement of formation and relative entropy of entanglement, proposing a method to derive REE from EOF for certain states, but not universally applicable.

Contribution

It introduces a new procedure to compute REE from EOF, applicable to specific symmetric mixed states, highlighting limitations for general states.

Findings

Procedure yields correct REE for symmetric states

Method fails for arbitrary mixed states

Highlights connection between EOF and REE in special cases

Abstract

It is well-known that entanglement of formation (EOF) and relative entropy of entanglement (REE) are exactly identical for all two-qubit pure states even though their definitions are completely different. We think this fact implies that there is a veiled connection between EOF and REE. In this context, we suggest a procedure, which enables us to compute REE from EOF without relying on the converse procedure. It is shown that the procedure yields correct REE for many symmetric mixed states such as Bell-diagonal, generalized Vedral-Plenino, and generalized Horodecki states. It also gives a correct REE for less symmetric Vedral-Plenio-type state. However, it is shown that the procedure does not provide correct REE for arbitrary mixed states.