Dynamics of the bounds of squared concurrence

Abstract

The dynamics of the quantum entanglement is a fundamental characteristic for various quantum systems. Since the computable entanglement measure for higher dimensional quantum states itself is absent, the dynamics of the entanglement expressed in an operational method will be of interest. We study the dynamics of $\ensuremath{\tau}$, an analytical lower bound of squared concurrence, of a bipartite $d\ensuremath{\bigotimes}d$ quantum state when one party goes through an arbitrary noisy channel. For a pure input state, the range of $\ensuremath{\tau}$ is obtained explicitly. For a mixed input state, an upper bound of $\ensuremath{\tau}$ is found. Interestingly, the tangle ${\ensuremath{\tau}}^{\ensuremath{'}}$, as an upper bound of squared concurrence, also has a similar dynamical property. Our results are similar to that of Konrad et al. and can help the estimation of high-dimension bipartite entanglement in experiments.