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Geometry and dynamics of one-norm geometric quantum discord

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Abstract

We investigate the geometry of one-norm geometric quantum discord and present a geometric interpretation of one-norm geometric quantum discord for a class of two-qubit states. It is found that one-norm geometric quantum discord has geometric behavior different from that described in Lang and Caves (Phys Rev Lett 105:150501, 2010), Li et al. (Phys Rev A 83:022321, 2011) and Yao et al. (Phys Lett A 376:358–364, 2012). We also compare the dynamics of the one-norm geometric quantum discord and other measures of quantum correlations under correlated noise. It is shown that different decoherent channels bring different influences to quantum correlations measured by concurrence, entropic quantum discord and geometric quantum discord, which depend on the memory parameter and decoherence parameter. We lay emphasis on the behaviors such as entanglement sudden death and sudden transition of quantum discord. Finally, we study the dynamical behavior of one-norm geometric quantum discord in one-dimensional anisotropic XXZ model by utilizing the quantum renormalization group method. It is shown that the one-norm geometric quantum discord demonstrates quantum phase transition through renormalization group approach.

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Acknowledgments

The authors are grateful to the referees for invaluable suggestions that help us improve the quality of the paper. This work is supported in part by the National Natural Science Foundation of China (Nos. 61272058, 61572532) and FCT PEst-OE/EEI/LA0008/2013 project, namely through the IT internal project CVQuantum.

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Authors and Affiliations

  1. Department of Computer Science, Sun Yat-sen University, Guangzhou, 510006, China

    Zhiming Huang & Daowen Qiu

  2. The Guangdong Key Laboratory of Information Security Technology, Sun Yat-sen University, Guangzhou, 510006, China

    Zhiming Huang & Daowen Qiu

  3. School of Economics and Management, Wuyi University, Jiangmen, 529020, China

    Zhiming Huang

  4. SQIG–Instituto de Telecomunicações, Departamento de Matemática, Instituto Superior Técnico, Av. Rovisco Pais, 1049-001, Lisbon, Portugal

    Paulo Mateus

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  1. Zhiming Huang
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Correspondence to Daowen Qiu.

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Huang, Z., Qiu, D. & Mateus, P. Geometry and dynamics of one-norm geometric quantum discord. Quantum Inf Process 15, 301–326 (2016). https://doi.org/10.1007/s11128-015-1176-9

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