How sharp are PV measures?

2007/01/11 by Anna Jenčová, A. Jencova, Sylvia Pulmannová +1
Computer Science · Mathematics · Physics and Astronomy · #Computability, Logic, AI Algorithms #Numerical Methods and Algorithms #Statistical Mechanics and Entropy #math-ph #math.MP #msc:81P10 #msc:81P15

paper · pdf · doi:10.1016/s0034-4877(07)80038-3

9 pages

arxiv created 2007/01/11 · openalex publication_date 2007/04/01 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Properties of sharp observables (normalized PV measures) in relation to smearing by a Markov kernel are studied. It is shown that for a sharp observable P defined on a standard Borel space, and an arbitrary observable M, the following properties are equivalent: (a) the range of P is contained in the range of M; (b) P is a function of M; (c) P is a smearing of M.

Citations

• Asymptotic performance of optimal state estimation in quantum two level system
• Operational Quantum Physics
• Positive operator measures, generalised imprimitivity theorem, and their applications
• The uncertainty relation for joint measurement of position and momentum