Two-qubit mixed states more entangled than pure states: Comparison of the relative entropy of entanglement for a given nonlocality

摘要

Amplitude damping changes entangled pure states into usually less-entangled mixed states.We show, however,nthat even local amplitude damping of one or two qubits can result in mixed states more entangled than purenstates if one compares the relative entropy of entanglement (REE) for a given degree of the Bell–Clauser-Horne-nShimony-Holt inequality violation (referred to as nonlocality). By applying Monte Carlo simulations, we find thenmaximally entangled mixed states and showthat they are likely to be optimal by checking the Karush-Kuhn-Tuckernconditions, which generalize the method of Lagrange multipliers for this nonlinear optimization problem. Wenshow that the REE for mixed states can exceed that of pure states if the nonlocality is in the range (0,0.82) and thenmaximal difference between theseREEs is 0.4.Aformer comparison [Phys. Rev. A 78, 052308 (2008)] of theREEnfor a given negativity showed analogous property but the corresponding maximal difference in the REEs is onenorder smaller (i.e., 0.039) and the negativity range is (0,0.53) only. For appropriate comparison, we normalizednthe nonlocality measure to be equal to the standard entanglement measures, including the negativity, for arbitraryntwo-qubit pure states. We also analyze the influence of the phase-damping channel on the entanglement of theninitially pure states. We show that the minimum of the REE for a given nonlocality can be achieved by thisnchannel, contrary to the amplitude-damping channel.