Abstract
We prove that the binegativity is always positive for any two-qubit state. As a result, and as suggested by previous work, the asymptotic relative entropy of entanglement in two qubits does not exceed the Rains bound, and the positive partial transposed-entanglement cost for any two-qubit state is determined to be the logarithmic negativity of the state. Further, the proof reveals some geometrical characteristics of the entangled states, and shows that partial transposition can give another separable approximation of the entangled state in two qubits.
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