We derive an analytical lower bound for the concurrence of tripartite quantum mixed states. A functional relation is established relating concurrence and the generalized partial transpositions.

BackgroundRecently, interest in phytochemicals from traditional Chinese medicinal herbs with the capability to inhibit cancer cells growth and proliferation has been growing rapidly due to their nontoxic nature. Dysosma versipellis as Bereridaceae plants is an endemic species in China, which has been proved to be an important Chinese herbal medicine because of its biological activity. However, systematic and comprehensive studies on the phytochemicals from Dysosma versipellis and their bioactivity are limited.ResultsFifteen compounds were isolated and characterized from the roots of Dysosma versipellis, among which six compounds were isolated from this plant for the first time. The inhibitory activities of these compounds were investigated on tumor cells PC3, Bcap-37 and BGC-823 in vitro by MTT method, and the results showed that podophyllotoxone (PTO) and 4'-demethyldeoxypodophyllotoxin (DDPT) had potent inhibitory activities against the growth of human carcinoma cell lines. Subsequent fluorescence staining and flow cytometry analysis indicated that these two compounds could induce apoptosis in PC3 and Bcap-37 cells, and the apoptosis ratios reached the peak (12.0% and 14.1%) after 72 h of treatment at 20 μM, respectively.ConclusionsThis study suggests that most of the compounds from the roots of D. versipellis could inhibit the growth of human carcinoma cells. In addition, PTO and DDPT could induce apoptosis of tumor cells.

Abstract. We investigate the lower bound of concurrence for multipartite quantum mixed states. Analytical lower bounds are derived for some multipartite systems, by establishing functional relations between concurrence and the generalized partial transpositions.

We study the concurrence of arbitrary dimensional bipartite quantum systems. An explicit analytical lower bound of concurrence is obtained which detects entanglement for some quantum states better than some wellknown separability criteria and improves the lower bounds, such as from the positive partial transposition, realignment criteria, and Breuer's entanglement witness.

We review some results on analytical computations of the measures for quantum entanglement: entanglement of formation and concurrence. We introduce some estimations of the lower bounds for the entanglement of formation in bipartite mixed states, and of lower bounds for the concurrence in bipartite and tripartite systems. The results on lower bounds for the concurrence are also generalized to arbitrary multipartite systems.