Sufficiency in quantum statistical inference

Details Sufficiency in quantum statistical inference Sufficiency in quantum statistical inference

2004-12-27

arxiv.org/abs/math-ph/0412093v1

Commun. Math. Phys. 263(2006), 259-276.

Physics

Mathematical Physics

Scientific paper

10.1007/s00220-005-1510-7

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.

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