The final publication is available at Springer via <a href="https://doi.org/10.1007/s10773-016-3068-x" target="_blank">https://doi.org/10.1007/s10773-016-3068-x</a>.
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dc.description.abstract
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.
en
dc.language
English
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dc.language.iso
en
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dc.publisher
Springer
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dc.relation.ispartof
International Journal of Theoretical Physics
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dc.rights.uri
http://creativecommons.org/licenses/by/4.0/
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dc.subject
Poset with an antitone involution
en
dc.subject
Quantum measurement
en
dc.subject
Multidimensional probability
en
dc.subject
Boolean orthoposet
en
dc.subject
Orthomodularity
en
dc.subject
Commutativity
en
dc.title
On bounded posets arising from quantum mechanical measurements
en
dc.type
Article
en
dc.type
Artikel
de
dc.rights.license
Creative Commons Namensnennung 4.0 International
de
dc.rights.license
Creative Commons Attribution 4.0 International
en
dc.rights.holder
The Author(s) 2016
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dc.type.category
Original Research Article
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tuw.journal.peerreviewed
true
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tuw.peerreviewed
true
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tuw.version
vor
-
dcterms.isPartOf.title
International Journal of Theoretical Physics
-
tuw.publication.orgunit
E104 - Institut für Diskrete Mathematik und Geometrie
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tuw.publisher.doi
10.1007/s10773-016-3068-x
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dc.date.onlinefirst
2016-06-22
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dc.identifier.eissn
1572-9575
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dc.identifier.libraryid
AC11360155
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dc.identifier.urn
urn:nbn:at:at-ubtuw:3-1914
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tuw.author.orcid
0000-0002-7030-4080
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dc.rights.identifier
CC BY 4.0
de
dc.rights.identifier
CC BY 4.0
en
wb.sci
true
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item.languageiso639-1
en
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Publications
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Publications
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http://purl.org/coar/resource_type/c_18cf
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item.openairecristype
http://purl.org/coar/resource_type/c_18cf
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item.fulltext
with Fulltext
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item.openaccessfulltext
Open Access
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item.grantfulltext
open
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item.openairetype
Article
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item.openairetype
Artikel
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crisitem.author.dept
E104 - Institut für Diskrete Mathematik und Geometrie
-
crisitem.author.dept
E104 - Institut für Diskrete Mathematik und Geometrie