Strong Converse and Stein's Lemma in the Quantum Hypothesis Testing

Abstract

The hypothesis testing problem of two quantum states is treated. We show a new inequality between the error of the first kind and the second kind, which complements the result of Hiai and Petz to establish the quantum version of Stein's lemma. The inequality is also used to show a bound on the first kind error when the power exponent for the second kind error exceeds the quantum relative entropy, and the bound yields the strong converse in the quantum hypothesis testing. Finally, we discuss the relation between the bound and the power exponent derived by Han and Kobayashi in the classical hypothesis testing.

LaTeX, 12 pages, submitted to IEEE Trans. Inform. Theory

Cited by in corpus (11)

• Complete entropic inequalities for quantum Markov chains
• A principle of maximum ignorance for semiclassical gravity
• A Quantum Multiparty Packing Lemma and the Relay Channel
• Decomposable coherence and quantum fluctuation relations
• Classical benchmarking for microwave quantum illumination
• Asymptotic relative submajorization of multiple-state boxes
• Quantum dichotomies and coherent thermodynamics beyond first-order asymptotics
• On the optimal certification of von Neumann measurements
• Limits to Perception by Quantum Monitoring with Finite Efficiency
• Performance of coherent-state quantum target detection in the context of asymmetric hypothesis testing
• The NP right-chiral $CC$ coupling constant estimation in neutrino oscillation experiments