Mathematical questions related to non-existence of hidden variables
Result description
The famous Gleason's Theorem gives a characterization of states on lattices of subspaces of Hilbert spaces. The attempts to simplify its proof have led to easy proofs of some consequences, mainly the non-existence of hidden variables (dispersion-free states). Here we simplify some of them. We also formulate related open problems concerning spaces with rational coordinates and group-valued measures.
Keywords
Gleason's TheoremBell inequalitiesBell's Geometrical LemmaPiron's Geometrical LemmaHilbert spacehidden variabledispersion-free statetwo-valued stateKochen-Specker theoremgroup-valued measure
The result's identifiers
Result code in IS VaVaI
Result on the web
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DOI - Digital Object Identifier
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Alternative languages
Result language
angličtina
Original language name
Mathematical questions related to non-existence of hidden variables
Original language description
The famous Gleason's Theorem gives a characterization of states on lattices of subspaces of Hilbert spaces. The attempts to simplify its proof have led to easy proofs of some consequences, mainly the non-existence of hidden variables (dispersion-free states). Here we simplify some of them. We also formulate related open problems concerning spaces with rational coordinates and group-valued measures.
Czech name
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Czech description
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Classification
Type
D - Article in proceedings
CEP classification
BA - General mathematics
OECD FORD branch
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Result continuities
Project
GA201/07/1051: Algebraic and measure-theoretic aspects of quantum structures
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2009
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Article name in the collection
Foundations of Probability and Physics - 5
ISBN
978-0-7354-0636-0
ISSN
0094-243X
e-ISSN
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Number of pages
8
Pages from-to
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Publisher name
American Institute of Physics
Place of publication
New York
Event location
Växjö
Event date
Aug 24, 2008
Type of event by nationality
WRD - Celosvětová akce
UT code for WoS article
000265432200017
Basic information
Result type
D - Article in proceedings
CEP
BA - General mathematics
Year of implementation
2009