46 research outputs found
Sufficiency in quantum statistical inference
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
Introduction to quantum Fisher information
The subject of this paper is a mathematical transition from the Fisher
information of classical statistics to the matrix formalism of quantum theory.
If the monotonicity is the main requirement, then there are several quantum
versions parametrized by a function. In physical applications the minimal is
the most popular. There is a one-to-one correspondence between Fisher
informations (called also monotone metrics) and abstract covariances. The skew
information and the chi-square-divergence are treated here as particular cases.Comment: 21 page