By investigating the property of the trace norm which appeared in the analytical lower bound for the concurrence of arbitrary dimensional bipartite quantum states [Phys. Rev. Lett. 95, 040504 (2005)], we demonstrate the limitation of the bound in that paper and provide several concrete examples.
We derive an analytical lower bound for the concurrence of a bipartite quantum state in arbitrary dimension. A functional relation is established relating concurrence, the Peres-Horodecki criterion, and the realignment criterion. We demonstrate that our bound is exact for some mixed quantum states. The significance of our method is illustrated by giving a quantitative evaluation of entanglement for many bound entangled states, some of which fail to be identified by the usual concurrence estimation method.