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arXiv · 0810.4045

Quantum hypothesis testing and sufficient subalgebras

Anna Jencova
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Abstract

We introduce a new notion of a sufficient subalgebra for quantum states: a subalgebra is 2- sufficient for a pair of states $\{ρ_0,ρ_1\}$ if it contains all Bayes optimal tests of $ρ_0$ against $ρ_1$. In classical statistics, this corresponds to the usual definition of sufficiency. We show this correspondence in the quantum setting for some special cases. Furthermore, we show that sufficiency is equivalent to 2 - sufficiency, if the latter is required for $\{ρ_0^{\otimes n},ρ_1^{\otimes}\}$, for all $n$.

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Anna Jencova. 2010-08-02. Quantum hypothesis testing and sufficient subalgebras. https://doi.org/10.1007/s11005-010-0398-0

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