Sufficiency in quantum statistical inference
Mathematical Physics
2009-11-10 v1 math.MP
Quantum Physics
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.
Cite
@article{arxiv.math-ph/0412093,
title = {Sufficiency in quantum statistical inference},
author = {Anna Jencova and Denes Petz},
journal= {arXiv preprint arXiv:math-ph/0412093},
year = {2009}
}