How sharp are PV measures?

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 $M$.

9 pages

References in corpus (2)

• Asymptotic performance of optimal state estimation in quantum two level system
• Positive operator measures, generalised imprimitivity theorem, and their applications

Cited by in corpus (2)

• Commutative POVMs and Fuzzy Observables
• Optimal covariant measurements: the case of a compact symmetry group and phase observables