Hierarchy and dynamics of trace distance correlationsTools Aaronson, Benjamin and Lo Franco, Rosario and Compagno, Giuseppe and Adesso, Gerardo (2013) Hierarchy and dynamics of trace distance correlations. New Journal of Physics, 15 . 093022/1093022/18. ISSN 13672630
Official URL: http://m.iopscience.iop.org/13672630/15/9/093022/
AbstractWe define and analyze measures of correlations for bipartite states based on trace distance. For Bell diagonal states of two qubits, in addition to the known expression for quantum correlations using this metric, we provide analytic expressions for the classical and total correlations. The ensuing hierarchy of correlations based on trace distance is compared to those based on relative entropy and Hilbert–Schmidt norm. Although some common features can be found, the trace distance measure is shown to differentiate from the others in that the closest uncorrelated state to a given bipartite quantum state is not given by the product of the marginals, and further, the total correlations are strictly smaller than the sum of the quantum and classical correlations. We compare the various correlation measures in two dynamical nonMarkovian models, locally applied phaseflip channels and random external fields. It is shown that the freezing behavior, observed across all known valid measures of quantum correlations for Bell diagonal states under local phaseflip channels, occurs for a larger set of starting states for the trace distance than for the other metrics.
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