Amplitude damping changes entangled pure states into usually less-entangledmixed states. We show, however, that even local amplitude damping of one or twoqubits can result in mixed states more entangled than pure states if onecompares the relative entropy of entanglement (REE) for a given degree of theBell-Clauser-Horne-Shimony-Holt inequality violation (referred to asnonlocality). By applying Monte-Carlo simulations, we find the maximallyentangled mixed states and show that they are likely to be optimal by checkingthe Karush-Kuhn-Tucker conditions, which generalize the method of Lagrangemultipliers for this nonlinear optimization problem. We show that the REE formixed states can exceed that of pure states if the nonlocality is in the range(0,0.82) and the maximal difference between these REEs is 0.4. A formercomparison [Phys. Rev. A 78, 052308 (2008)] of the REE for a given negativityshowed analogous property but the corresponding maximal difference in the REEsis one-order smaller (i.e., 0.039) and the negativity range is (0,0.53) only.For appropriate comparison, we normalized the nonlocality measure to be equalto the standard entanglement measures, including the negativity, for arbitrarytwo-qubit pure states. We also analyze the influence of the phase-dampingchannel on the entanglement of the initially pure states. We show that theminimum of the REE for a given nonlocality can be achieved by this channel,contrary to the amplitude damping channel.
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