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Binegativity and geometry of entangled states in two qubits
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We prove that the binegativity is always positive for any two-qubit state. As a result, as suggested by the previous works, the asymptotic relative entropy of entanglement in two qubits does not exceed the Rains bound, and the PPT-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 the partial transposition can give another separable approximation of the entangled state in two qubits.
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Logarithmic negativity typically equals exact entanglement cost
Logarithmic negativity equals exact entanglement cost under PPT-preserving operations for large random induced mixed states.
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