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

TL;DR

This paper demonstrates that local amplitude damping can produce mixed two-qubit states with higher relative entropy of entanglement than pure states at the same nonlocality level, challenging conventional expectations.

Contribution

It introduces a comparison of REE for mixed and pure states at fixed nonlocality, revealing that mixed states can be more entangled than pure states under certain conditions.

Findings

Mixed states can have higher REE than pure states for nonlocality in (0,0.82).

Maximal REE difference between mixed and pure states is 0.4.

Amplitude damping can increase entanglement beyond pure states at the same nonlocality.

Abstract

Amplitude damping changes entangled pure states into usually less-entangled mixed states. We show, however, that even local amplitude damping of one or two qubits can result in mixed states more entangled than pure states if one compares the relative entropy of entanglement (REE) for a given degree of the Bell-Clauser-Horne-Shimony-Holt inequality violation (referred to as nonlocality). By applying Monte-Carlo simulations, we find the maximally entangled mixed states and show that they are likely to be optimal by checking the Karush-Kuhn-Tucker conditions, which generalize the method of Lagrange multipliers for this nonlinear optimization problem. We show that the REE for mixed 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 former comparison [Phys. Rev. A 78, 052308 (2008)] of the REE for a given negativity showed analogous property but the corresponding maximal difference in the REEs is 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 equal to the standard entanglement measures, including the negativity, for arbitrary two-qubit pure states. We also analyze the influence of the phase-damping channel on the entanglement of the initially pure states. We show that the minimum of the REE for a given nonlocality can be achieved by this channel, contrary to the amplitude damping channel.