Quantum hypothesis testing and sufficient subalgebras

Details Quantum hypothesis testing and sufficient subalgebras Quantum hypothesis testing and sufficient subalgebras

2008-10-22

arxiv.org/abs/0810.4045v2

Lett. Math. Phys 93 (2010), 15

Physics

Quantum Physics

12 pages

Scientific paper

We introduce a new notion of a sufficient subalgebra for quantum states: a subalgebra is 2- sufficient for a pair of states $\{\rho_0,\rho_1\}$ if it contains all Bayes optimal tests of $\rho_0$ against $\rho_1$. 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 $\{\rho_0^{\otimes n},\rho_1^{\otimes}\}$, for all $n$.

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