Relative Entropy of Entanglement for Two-Qubit State with $z$-directional Bloch Vectors

TL;DR

This paper introduces a method to compute the relative entropy of entanglement for two-qubit states with z-directional Bloch vectors, providing a practical approach for a class of states where no closed-form solution exists.

Contribution

The paper presents a novel method for deriving the relative entropy of entanglement specifically for two-qubit states with z-directional Bloch vectors, expanding computational tools in quantum information.

Findings

Method guarantees derivation for most such states

Closest separable states also have z-directional Bloch vectors

Few exceptions where the method does not apply

Abstract

So far there is no closed formula for relative entropy of entanglement of arbitrary two-qubit states. In this paper we present a method, which guarantees the derivation of the relative entropy of entanglement for most states that have $z$-directional Bloch vectors. It is shown that the closest separable states for those states also have $z$-directional Bloch vectors though there are few exceptions.