Maximally entangled mixed states under nonlocal unitary operations in two qubits

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Abstract
We propose mixed states in two qubits that have a property that the amount of entanglement of these states cannot be increased by any unitary transformation. The property is proven when the rank of the states is less than 4, and confirmed numerically in the other general cases. The corresponding entanglement of formation specified by its eigenvalues gives an upper bound of that for density matrices with the same eigenvalues. Further, as a simple application of the upper bound of the entanglement of formation, we analyze the entanglement of formation of the state generated by a decohered controlled-NOT gate in the spin-boson model.
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