Abstract
It is strictly proved that a two-qubit [Formula: see text]-invariant state reaches its relative entropy of entanglement (REE) by the separable state having the same matrix structure. We also formulate three quadratic equations for the corresponding closest separable state (CSS) of [Formula: see text]-invariant states by their symmetric property. Thus, the CSS of [Formula: see text]-invariant state can be provided. Furthermore, to illustrate our result we consider two concrete examples.
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