Quantum discord and one-norm geometric quantum discord for XXX Heisenberg spin chain under noisy channels

Abstract

Here, we compare the behavior of the quantum discord, 1-norm geometric quantum discord and concurrence under the effect of decoherence for XXX Heisenberg spin chain. Their dependencies on temperature and coupling constant are presented in detail. By a comparison between them we can see that quantum discord and 1-norm geometric quantum discord are more robust than the concurrence against decoherence in the sense that quantum discord and 1-norm geometric quantum discord takes a nonzero value and decrease asymptotically, while the concurrence is zero in a large range of parameters including temperature and coupling constant. Moreover, we find that there is no simple relative ordering between 1-norm geometric quantum discord and quantum discord. This result contradicts the information which provided in some papers.