Hierarchy and dynamics of trace distance correlations

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

Abstract

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.

Citation

Aaronson, B., Lo Franco, R., Compagno, G., & Adesso, G. (2013). Hierarchy and dynamics of trace distance correlations. New Journal of Physics, 15, Article 093022. https://doi.org/10.1088/1367-2630/15/9/093022

• 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
• DOI: https://doi.org/10.1088/1367-2630/15/9/093022
• Public URL: https://nottingham-repository.worktribe.com/output/717876
• Publisher URL: http://m.iopscience.iop.org/1367-2630/15/9/093022/