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This paper attempts to develop a theory of sufficiency in the setting of non-commutative algebras parallel to the ideas in
classical mathematical statistics. Sufficiency of a coarse-graining means that all information is extracted about the mutual
relation of a given family of states. In the paper sufficient coarse-grainings are characterized in several equivalent ways
and the non-commutative analogue of the factorization theorem is obtained. As an application we discuss exponential families.
Our factorization theorem also implies two further important results, previously known only in finite Hilbert space dimension,
but proved here in generality: the Koashi-Imoto theorem on maps leaving a family of states invariant, and the characterization
of the general form of states in the equality case of strong subadditivity.
Supported by the EU Research Training Network Quantum Probability with Applications to Physics, Information Theory and Biology
and Center of Excellence SAS Physics of Information I/2/2005.
Supported by the Hungarian grant OTKA T032662 相似文献
56.
Clément Gallo 《Comptes Rendus Mathematique》2006,342(5):319-323
We give an upper bound on the growth rate of the Schrödinger group on Zhidkov spaces. In dimension 1, we prove that this bound is sharp. To cite this article: C. Gallo, C. R. Acad. Sci. Paris, Ser. I 342 (2006). 相似文献
57.
We study the asymptotic properties of the Bayes estimator in models differentiable in quadratic mean (DQM) in the case of
independent and identically distributed observations. The goal is to define weak assumptions on the model under which this
estimator is asymptotically efficient, regular, and asymptotically of minimal risk. The results of the paper are applied to
models based on a mixture distribution, the Cauchy distribution with location and scale parameter, and the Weibull distribution.
Bibliography: 10 titles.
Published in Zapiski Nauchnykh Seminarov POMI, Vol. 328, 2005, pp. 114–146. 相似文献
58.
A. I. Magunov A. Ya. Faenov I. Yu. Skobelev T. A. Pikuz E. Biémont P. Quinet F. Blasco C. Bonte F. Dorchies T. Caillaud F. Salin C. Stenz 《Journal of Experimental and Theoretical Physics》2002,95(6):998-1005
The satellite structure of 1s2p 1,3 P 1-1s 21 S 0 lines of the He-like argon ion in plasma produced by a 45-fs laser pulse in a gas-jet cluster target is measured with a high spectral resolution. Radiation transitions 2p → 1s from autoionizing states (AISs) are detected for ions ranging from Li-like to F-like. The spectrum observed is theoretically simulated with the use of the spectroscopic data for the AISs of multicharged ions obtained within the multiconfiguration relativistic Hartree-Fock method. Good agreement with experimental data is obtained when the main population channels of these states are taken into account for typical values of cluster-target plasma parameters. 相似文献
59.
Michel Hébert 《Archive for Mathematical Logic》1991,31(2):133-143
Summary We give a syntactic characterization of (finitary) theories whose categories of models are closed under the formation of connected limits (respectively the formation of pullbacks and substructures) in the category of all structures. They are also those theories whose consistent extensions by new atomic facts admit in each component an initial structure (respectively an initial term structure), and also thoseT for whichM(T) is locally finitely multi-presentable in a canonical way. We also show that these two properties of theories are nonuniform. 相似文献
60.