Quantum hypothesis testing and sufficient subalgebras

Abstract

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 $n$.

12 pages

References in corpus (3)

• The Quantum Chernoff Bound
• Asymptotic Error Rates in Quantum Hypothesis Testing
• The Chernoff lower bound for symmetric quantum hypothesis testing

Cited by in corpus (7)

• Quantum f-divergences and error correction
• Principles of Quantum Communication Theory: A Modern Approach
• Reversibility conditions for quantum operations
• Recoverability of quantum channels via hypothesis testing
• Comparison of quantum binary experiments
• Multiple Quantum Hypothesis Testing Expressions and Classical-Quantum Channel Converse Bounds
• Generalized conditional expectations for quantum retrodiction and smoothing