Unsharpness, Naimark theorem and informational equivalence of quantum observables

DOI10.1007/S10773-009-0219-3zbMath1204.81022OpenAlexW2029822082MaRDI QIDQ616809

Roberto Beneduci

Publication date: 12 January 2011

Published in: International Journal of Theoretical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10773-009-0219-3

zbMATH Keywords

POV measuresinformational contentNaimark theorem

Mathematics Subject Classification ID

Vector-valued set functions, measures and integrals (28B05) Selfadjoint operator theory in quantum theory, including spectral analysis (81Q10) Vector-valued measures and integration (46G10) Measures of information, entropy (94A17) Nonselfadjoint operator theory in quantum theory including creation and destruction operators (81Q12) Quantum state spaces, operational and probabilistic concepts (81P16)

Related Items (10)

Positive operator valued measures and Feller Markov kernels ⋮ Fuzzy observables: from weak Markov kernels to Markov kernels ⋮ An effective iterative method to build the Naimark extension of rank-n POVMs ⋮ On the relationships between the moments of a POVM and the generator of the von Neumann algebra it generates ⋮ Uniform continuity of POVMs ⋮ Joint measurability through Naimark's dilation theorem ⋮ Universal randomization of quantum observables ⋮ Stochastic matrices and a property of the infinite sequences of linear functionals ⋮ Commutative POV-measures: from the Choquet representation to the Markov kernel and back ⋮ Space localization of the photon

Cites Work

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• Optimal measurements in quantum mechanics
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• How sharp are PV measures
• An operational approach to quantum probability
• From unsharp to sharp quantum observables: The general Hilbert space case
• NEUMARK'S OPERATORS AND SHARP RECONSTRUCTIONS
• A geometrical characterization of commutative positive operator valued measures
• Neumark operators and sharp reconstructions: The finite dimensional case
• Operator integrals and phase space observables
• Sharp reconstruction of unsharp quantum observables
• Operational Quantum Physics
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