2005/08/31 by Åsa Ericsson, Asa Ericsson
Computer Science · Physics and Astronomy · #Gaussian Processes and Bayesian Inference #Quantum Mechanics and Applications #Statistical Mechanics and Entropy #quant-ph
paper · pdf · doi:10.1088/0305-4470/38/44/l01
published as J. Phys. A: Math. Gen. 38 (2005) L725-L730 · 3 pages, replaced by published version
arxiv created 2005/10/19 · openalex publication_date 2005/10/19 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/04
From statistical distinguishability of probability distributions, one can define distinguishability of quantum states. A corresponding measurement to perform, optimal in a definite sense, for distinguishing between two given states ρ A and ρ B , has been derived by Fuchs and Caves. We show that the Bures–Uhlmann geodesic through the two states singles out this measurement. The geodesic ‘bounces’ at the boundary of the set of quantum states. Whenever the geodesic hits the boundary, the state orthogonal to that boundary state is one of the basis states for the measurement.