Abstract
Hasegawa and Petz introduced the notion of paired monotone metrics. They also gave a characterisation theorem showing that Wigner-Yanase-Dyson metrics are the only members of the paired family. In this paper we show that the characterisation theorem holds true under hypotheses that are more general than those used in the above quoted references.
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Gibilisco, P., Isola, T. On the characterisation of paired monotone metrics. Ann Inst Stat Math 56, 369–381 (2004). https://doi.org/10.1007/BF02530551
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DOI: https://doi.org/10.1007/BF02530551