Abstract
The classical Fisher information is superadditive in the sense that the Fisher information of a bivariate probability density is always not less than the sum of those of the marginals. The longstanding conjecture concerning the superadditivity of the Wigner–Yanase–Dyson information is a quantum analogue of this property. It is remarkable that Hansen constructed a numerical counterexample to the quantum case (J. Stat. Phys. 126: 643–648, 2007). However, the requirement of superadditivity of an information-theoretic quantity such as the Wigner–Yanase–Dyson information seems so intuitive, it is desirable to identify conditions as general as possible such that the superadditivity holds. In this paper, we establish the superadditivity in several physically significant cases.
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Luo, S. Notes on Superadditivity of Wigner–Yanase–Dyson Information. J Stat Phys 128, 1177–1188 (2007). https://doi.org/10.1007/s10955-007-9349-2
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DOI: https://doi.org/10.1007/s10955-007-9349-2