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 (7)

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• Optimal measurements in quantum mechanics
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• The uncertainty relation for joint measurement of position and momentum
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Cited by in corpus (16)

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• Robustness of incompatibility for quantum devices
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• Sequential measurements of conjugate observables
• Positive Operator Valued Measures and Feller Markov Kernels
• Compatibility properties of extreme quantum observables
• Order preserving maps on quantum measurements
• Extreme commutative quantum observables are sharp
• Topologies on Quantum Effects
• Notes on Deterministic Programming of Quantum Observables and Channels
• Optimal covariant measurements: the case of a compact symmetry group and phase observables
• Semispectral Measures and Feller markov Kernels
• Limitations on post-processing assisted quantum programming
• Two-moment characterization of spectral measures on the real line
• Uniform continuity of POVMs
• Compressing continuous variable quantum measurements