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Metric-Adjusted Skew Information: Convexity and Restricted Forms of Superadditivity

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Abstract

We give a truly elementary proof of the convexity of metric-adjusted skew information following an idea of Effros. We extend earlier results of weak forms of superadditivity to general metric-adjusted skew information. Recently, Luo and Zhang introduced the notion of semi-quantum states on a bipartite system and proved superadditivity of the Wigner–Yanase–Dyson skew informations for such states. We extend this result to the general metric-adjusted skew information. We finally show that a recently introduced extension to parameter values 1 < p ≤ 2 of the WYD-information is a special case of (unbounded) metric-adjusted skew information.

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Authors and Affiliations

  1. Department of Mathematics, Beijing Institute of Technology, Beijing, China

    Liang Cai

  2. Department of Economics, University of Copenhagen, Øster Farimagsgade 5, Building 26, 1353, Copenhagen K, Denmark

    Frank Hansen

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  1. Liang Cai
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  2. Frank Hansen
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Correspondence to Frank Hansen.

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Cai, L., Hansen, F. Metric-Adjusted Skew Information: Convexity and Restricted Forms of Superadditivity. Lett Math Phys 93, 1–13 (2010). https://doi.org/10.1007/s11005-010-0396-2

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  • DOI: https://doi.org/10.1007/s11005-010-0396-2

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