A Kolmogorov Extension Theorem for POVMs |
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Authors: | Roderich Tumulka |
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Institution: | (1) Department of Mathematics, Rutgers University, 110 Frelinghuysen Road, Piscataway, NJ 08854-8019, USA |
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Abstract: | We 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 satisfies the consistency (or projectivity) condition then there is a POVM G on the space 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.
The main proof in this article was first formulated in my habilitation thesis 6]. |
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Keywords: | 81Q99 46N50 |
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