Evolution of entanglement for quantum mixed states

A simple relation is introduced for concurrence to describe how much the entanglement of bipartite system is at least left if either (or both) subsystem undergoes an arbitrary physical process. This provides a lower bound for concurrence of mixed states (pure states are included) in contrast to the upper bound given by Konrad et al [Nature Physics \textbf{4}, 99 (2008)]. Our results are also suitable for a general high dimensional bipartite quantum systems.