On the factorization criterion for quantum statistics

Rok, strany: 2005, 373 - 380

We discuss some fundamental statistical notions for a quantum system in the simplest case when only a finite number of different states is possible and all states are pure. Thus our non-commutative statistical space is described by a Hilbert space $H$ with a finite system of unit vectors $(φ_θ, θ =1,…, n)$. Each statistic is described by a self-adjoint operator $S$ in $H$. We define the sufficiency of $S$ in some natural way motivated by the classical factorization criterion. We show that a generalization of Blackwell-Rao theorem cannot be obtained. Moreover, some linear space containing all non-biased estimators with minimal variance is described in the paper. In fact, this space is huge, compared to the commutative case.

ISO 690:

Czkwianianc, E. 2005. On the factorization criterion for quantum statistics. In Mathematica Slovaca, vol. 55, no.3, pp. 373-380. 0139-9918.

APA:

Czkwianianc, E. (2005). On the factorization criterion for quantum statistics. Mathematica Slovaca, 55(3), 373-380. 0139-9918.