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On bounded posets arising from quantum mechanical measurements
AuthorLänger, Helmut In der Gemeinsamen Normdatei der DNB nachschlagen ; Dorninger, Dietmar In der Gemeinsamen Normdatei der DNB nachschlagen
Published in
International Journal of Theoretical Physics, 2016, Vol. 55, Issue 10, page 4453-4461
PublishedSpringer US, 2016
Published version
Document typeJournal Article
Keywords (EN)Poset with an antitone involution / Quantum measurement / Multidimensional probability / Boolean orthoposet / Orthomodularity / Commutativity
URNurn:nbn:at:at-ubtuw:3-1914 Persistent Identifier (URN)
 The work is publicly available
On bounded posets arising from quantum mechanical measurements [0.18 mb]
Abstract (English)

Let S be a set of states of a physical system. The probabilities p(s) of the occurrence of an event when the system is in different states s S define a function from S to [0, 1] called a numerical event or, more precisely, an S-probability. If one orders a set P of S-probabilities in respect to the order of functions, further includes the constant functions 0 and 1 and defines p′ = 1 p for every p P, then one obtains a bounded poset of S-probabilities with an antitone involution. We study these posets in respect to various conditions about the existence of the sum of certain functions within the posets and derive properties from these conditions. In particular, questions of relations between different classes of S-probabilities arising this way are settled, algebraic representations are provided and the property that two S-probabilities commute is characterized which is essential for recognizing a classical physical system.

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