Typical features of the Mintert-Buchleitner lower bound for concurrence.
Borras, A.; Majtey, A.P.; Plastino, A.R.; Casas, M. and Plastino, A.
Physical Review A 79, 022112 (1-6) (2009)
Despite the great importance of quantum entanglement, a computationally practical, physically motivated, and experimentally implementable way to estimate the amount of entanglement associated with a general (mixed) state of a bipartite quantum system is still lacking. An entanglement lower bound recently advanced by Mintert and Buchleitner [Phys. Rev. Lett. 98, 140505 (2007)] was proposed as a possible tool for the aforementioned task. Mintert and Buchleitner presented evidence indicating that, due to its tightness, in some important cases the alluded bound can be used as an entanglement measure. From the physical point of view, what makes this bound particularly appealing as an entanglement measure is that it is based on an observable quantity. For this last reason, and also because of its other attractive feature, mathematical simplicity, this promising bound and its possible use as an entanglement estimator certainly deserve to be the focus of careful attention. The usefulness of the bound as an entanglement measure, however, depends on its degree of tightness. Here we perform a systematic survey of the behavior of the alluded bound in state space, in order to determine its typical properties (in particular its tightness) and thus assess its value as an entanglement estimator.