2020/08/01 by Marcin Jarzyna, Jan Kolodynski
Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Fiducial inference #Focus (optics) #Inference #Information geometry #Quantum #Quantum Mechanics and Applications #Quantum probability #Statistical Mechanics and Entropy #Statistical distance #Statistical hypothesis testing #Statistical inference #Statistical model #quant-ph
paper · pdf · doi:10.1109/jsait.2020.3017469
published as IEEE Journal on Selected Areas in Information Theory 1(2), 367-386 (2020) · 20 pages (+ bibliography), accepted for publication in IEEE Journal on Selected Areas in Information Theory
openalex publication_date 2020/08/01 · arxiv created 2020/08/31 · openalex created_date 2020/09/01 · arxiv updated 2020/09/25 · openalex updated_date 2026/08/05
We study quantum statistical inference tasks of hypothesis testing and their canonical variations, in order to review relations between their corresponding figures of merit-measures of statistical distance-and demonstrate the crucial differences which arise in the quantum regime in contrast to the classical setting. In our analysis, we primarily focus on the geometric approach to data inference problems, within which the aforementioned measures can be neatly interpreted as particular forms of divergences that quantify distances in the space of probability distributions or, when dealing with quantum systems, of density matrices. Moreover, with help of the standard language of Riemannian geometry we identify both the metrics such divergences must induce and the relations such metrics must then naturally inherit. Finally, we discuss exemplary applications of such a geometric approach to problems of quantum parameter estimation, “speed limits” and thermodynamics.