238 research outputs found
Quantum local asymptotic normality based on a new quantum likelihood ratio
We develop a theory of local asymptotic normality in the quantum domain based
on a novel quantum analogue of the log-likelihood ratio. This formulation is
applicable to any quantum statistical model satisfying a mild smoothness
condition. As an application, we prove the asymptotic achievability of the
Holevo bound for the local shift parameter.Comment: Published in at http://dx.doi.org/10.1214/13-AOS1147 the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org
Autoparallelity of Quantum Statistical Manifolds in The Light of Quantum Estimation Theory
In this paper we study the autoparallelity w.r.t. the e-connection for an
information-geometric structure called the SLD structure, which consists of a
Riemannian metric and mutually dual e- and m-connections, induced on the
manifold of strictly positive density operators. Unlike the classical
information geometry, the e-connection has non-vanishing torsion, which brings
various mathematical difficulties. The notion of e-autoparallel submanifolds is
regarded as a quantum version of exponential families in classical statistics,
which is known to be characterized as statistical models having efficient
estimators (unbiased estimators uniformly achieving the equality in the
Cramer-Rao inequality). As quantum extensions of this classical result, we
present two different forms of estimation-theoretical characterizations of the
e-autoparallel submanifolds. We also give several results on the
e-autoparallelity, some of which are valid for the autoparallelity w.r.t. an
affine connection in a more general geometrical situation
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