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Hierarchy and dynamics of trace distance correlations

Aaronson, Benjamin; Lo Franco, Rosario; Compagno, Giuseppe; Adesso, Gerardo

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Benjamin Aaronson

Rosario Lo Franco

Giuseppe Compagno


We 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 non-Markovian models, locally applied phase-flip 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 phase-flip channels, occurs for a larger set of starting states for the trace distance than for the other metrics.


Aaronson, B., Lo Franco, R., Compagno, G., & Adesso, G. (2013). Hierarchy and dynamics of trace distance correlations. New Journal of Physics, 15, Article 093022.

Journal Article Type Article
Publication Date Sep 13, 2013
Deposit Date Apr 1, 2014
Publicly Available Date Apr 1, 2014
Journal New Journal of Physics
Electronic ISSN 1367-2630
Publisher IOP Publishing
Peer Reviewed Peer Reviewed
Volume 15
Article Number 093022
Public URL
Publisher URL


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