10 research outputs found
On the characterisation of paired monotone metrics
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.Comment: 12 pages, to appear on Ann. Inst. Stat. Math.; v2: changes made to
conform to accepted version, title changed as wel
Two quantum analogues of Fisher information from a large deviation viewpoint of quantum estimation
We discuss two quantum analogues of Fisher information, symmetric logarithmic
derivative (SLD) Fisher information and Kubo-Mori-Bogoljubov (KMB) Fisher
information from a large deviation viewpoint of quantum estimation and prove
that the former gives the true bound and the latter gives the bound of
consistent superefficient estimators. In another comparison, it is shown that
the difference between them is characterized by the change of the order of
limits.Comment: LaTeX with iopart.cls, iopart12.clo, iopams.st