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

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.

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