Eur. Phys. J. D (2014) 68: 274
https://doi.org/10.1140/epjd/e2014-50387-8

Regular Article

Correlation evolution and monogamy of two geometric quantum discords in multipartite systems

¹ College of Physical Science and Information Engineering and Hebei Advance Thin Films Laboratory, Hebei Normal University, Shijiazhuang, Hebei 050024, P.R. China
² Department of Physics and Center of Theoretical and Computational Physics, The University of Hong Kong, Pokfulam Road, Hong Kong, P.R. China

^a e-mail: ykbai@semi.ac.cn
^b e-mail: zwang@hku.hk

Received: 15 May 2014
Received in final form: 6 July 2014
Published online: 1 October 2014

Abstract

We explore two different geometric quantum discords defined respectively via the trace norm (GQD-1) and Hilbert-Schmidt norm (GQD-2) in multipartite systems. A rigorous hierarchy relation is revealed for the two GQDs in a class of symmetric two-qubit X-shape states. For multiqubit pure states, it is found that both GQDs are related to the entanglement concurrence, with the hierarchy relation being saturated. Furthermore, we look into a four-partite dynamical system consisting of two cavities interacting with independent reservoirs. It is found that the GQD-2 can exhibit various sudden change behaviours, while the GQD-1 only evolves asymptotically, with the two GQDs exhibiting different monogamous properties.