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Superadditivity of Wigner-Yanase-Dyson Information Revisited

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Abstract

The Wigner-Yanase-Dyson information is an important variant of quantum Fisher information. Two fundamental requirements concerning this notion of information content originally postulated by Wigner and Yanase are convexity and superadditivity. The former was fully established by Lieb in 1973, and led to the first proof of the strong subadditivity of quantum entropy. The latter, although widely believed to be true, was quite recently disproved by Hansen. Nevertheless, superadditivity has also been established in two extreme cases, i.e., when the states are pure or classical. In this paper, we first review a scheme to classify bipartite states into a hierarchy of classical, semi-quantum, and quantum states, which are arranged in the order of increasing quantumness. We then prove the superadditivity of the Wigner-Yanase-Dyson information for all semi-quantum states. The convexity of the Wigner-Yanase-Dyson information plays a crucial role here.

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Authors and Affiliations

  1. Academy of Mathematics and Systems Science, Chinese Academy of Sciences, 100190, Beijing, People’s Republic of China

    Shunlong Luo

  2. Department of Mathematics, City University of Hong Kong, Hong Kong, People’s Republic of China

    Qiang Zhang

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  1. Shunlong Luo
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  2. Qiang Zhang
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Correspondence to Shunlong Luo.

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Luo, S., Zhang, Q. Superadditivity of Wigner-Yanase-Dyson Information Revisited. J Stat Phys 131, 1169–1177 (2008). https://doi.org/10.1007/s10955-008-9534-y

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  • DOI: https://doi.org/10.1007/s10955-008-9534-y

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