Q-Math Seminar
Non-Asymptotic Bounds for Quantum Hypothesis Testing
Speaker: Gonzalo Vázquez-Villar (UC3M, Signal Processing Group)Date: Wednesday, 11 March 2026 - 11:00Place: Aula 2.2 D08, Campus de Leganés, Universidad Carlos III de Madrid
Online: meet.google.com/ejj-hfpf-xuw
Abstract:
Quantum hypothesis testing, the task of distinguishing quantum states through measurement, is central to quantum information theory, with applications ranging from quantum communication to quantum error correction. In this talk, we formalize the binary quantum hypothesis testing problem in both non-asymptotic and asymptotic settings. A central tool in our analysis is the Nussbaum-Szkoła mapping, which transforms the quantum problem into a classical surrogate test. Using this mapping, we derive rigorous non-asymptotic converse bounds on the error probabilities of quantum hypothesis testing and provide a unified treatment of three key asymptotic regimes: small, moderate, and large deviations. Furthermore, we show that the M-ary quantum hypothesis testing problem admits an exact binary formulation, reducing the analysis of its minimum average error probability to a single binary hypothesis test with a structured alternative hypothesis. Overall, this talk illustrates how classical methodologies can provide both intuitive insight and powerful analytical tools for understanding quantum hypothesis testing and related quantum information processing tasks.
