On the characterisation of paired monotone metrics

Abstract

Hasegawa and Petz introduced the notion of dual statistically monotone metrics. They also gave a characterisation theorem showing that Wigner-Yanase-Dyson metrics are the only members of the dual family. In this paper we show that the characterisation theorem holds true under more general hypotheses.

12 pages, to appear on Ann. Inst. Stat. Math.; v2: changes made to conform to accepted version, title changed as well