Gleason-Type Derivations of the Quantum Probability Rule for Generalized Measurements

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dc.creatorCaves, Carlton M.
dc.creatorFuchs, Christopher A.
dc.creatorManne, Kiran
dc.creatorRenes, Joseph M.
dc.date2003-06-26
dc.date.accessioned2026-07-07T06:30:36Z
dc.date.available2026-07-07T06:30:36Z
dc.descriptionWe prove a Gleason-type theorem for the quantum probability rule using frame functions defined on positive-operator-valued measures (POVMs), as opposed to the restricted class of orthogonal projection-valued measures used in the original theorem. The advantage of this method is that it works for two-dimensional quantum systems (qubits) and even for vector spaces over rational fields--settings where the standard theorem fails. Furthermore, unlike the method necessary for proving the original result, the present one is rather elementary. In the case of a qubit, we investigate similar results for frame functions defined upon various restricted classes of POVMs. For the so-called trine measurements, the standard quantum probability rule is again recovered.
dc.description10 pages RevTeX, no figures
dc.identifierhttps://arxiv.org/abs/quant-ph/0306179
dc.identifierhttp://arxiv.org/abs/quant-ph/0306179
dc.identifierFound. Phys. 34, 193 (2004)
dc.identifierdoi:10.1023/B:FOOP.0000019581.00318.a5
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/98380
dc.subjectQuantum Physics
dc.titleGleason-Type Derivations of the Quantum Probability Rule for Generalized Measurements
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