A Kolmogorov Extension Theorem for POVMs

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dc.creatorTumulka, Roderich
dc.date2007-10-18
dc.date.accessioned2026-07-07T10:17:34Z
dc.date.available2026-07-07T10:17:34Z
dc.descriptionWe prove a theorem about positive-operator-valued measures (POVMs) that is an analog of the Kolmogorov extension theorem, a standard theorem of probability theory. According to our theorem, if a sequence of POVMs G_n on $\mathbb{R}^n$ satisfies the consistency (or projectivity) condition $G_{n+1}(A\times \mathbb{R}) = G_n(A)$ then there is a POVM G on the space $\mathbb{R}^\mathbb{N}$ of infinite sequences that has G_n as its marginal for the first n entries of the sequence. We also describe an application in quantum theory.
dc.description6 pages LaTeX, no figures
dc.identifierhttps://arxiv.org/abs/0710.3605
dc.identifierhttp://arxiv.org/abs/0710.3605
dc.identifierLetters in Mathematical Physics 84 (2008) 41-46
dc.identifierdoi:10.1007/s11005-008-0229-8
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/173894
dc.subjectMathematical Physics
dc.subjectQuantum Physics
dc.subject81Q99; 46N50
dc.titleA Kolmogorov Extension Theorem for POVMs
dc.typetext

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