How sharp are PV measures?

Details How sharp are PV measures? How sharp are PV measures?

2007-01-11

arxiv.org/abs/math-ph/0701031v1

Physics

Mathematical Physics

9 pages

Scientific paper

10.1016/S0034-4877(07)80038-3

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 $M$.

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