Geometric discord of tripartite quantum systems

Abstract

We study the quantification of geometric discord for tripartite quantum systems. Firstly, we obtain the analytic formula of geometric discord for tripartite pure states. It is already known that the geometric discord of pure states reduces to the geometric entanglement in bipartite systems, the results presented here show that this property is no longer true in tripartite systems. Furthermore, we provide an operational meaning for tripartite geometric discord by linking it to quantum state discrimination, that is, we prove that the geometric discord of tripartite states is equal to the minimum error probability to discriminate a set of quantum states with von Neumann measurement. Lastly, we calculate the geometric discord of three-qubit Bell diagonal states and then investigate the dynamic behavior of tripartite geometric discord under local decoherence. It is interesting that the frozen phenomenon exists for geometric discord in this scenario.