%0 Generic %1 citeulike:34604 %A Jencova, Anna %A Petz, Denes %D 2004 %K classical mathematics statistics sufficiency %T Sufficiency in quantum statistical inference %U http://arxiv.org/abs/math-ph/0412093 %X 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. Among the applications the equality case for the strong subadditivity of the von Neumann entropy, the Imoto-Koashi theorem and exponential families are treated. The setting of the paper allows the underlying Hilbert space to be infinite dimensional.

@misc{citeulike:34604, abstract = {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. Among the applications the equality case for the strong subadditivity of the von Neumann entropy, the Imoto-Koashi theorem and exponential families are treated. The setting of the paper allows the underlying Hilbert space to be infinite dimensional.}, added-at = {2007-08-18T13:22:24.000+0200}, author = {Jencova, Anna and Petz, Denes}, biburl = {https://www.bibsonomy.org/bibtex/2730c49fde0c61aa39be5d92cc97545c1/a_olympia}, citeulike-article-id = {34604}, description = {citeulike}, eprint = {math-ph/0412093}, interhash = {cc0aab31e1f4ae63ea8071438dc8cf16}, intrahash = {730c49fde0c61aa39be5d92cc97545c1}, keywords = {classical mathematics statistics sufficiency}, month = {December}, timestamp = {2007-08-18T13:23:00.000+0200}, title = {Sufficiency in quantum statistical inference}, url = {http://arxiv.org/abs/math-ph/0412093}, year = 2004 }