Quantum Logics that are Symmetric-difference-closed

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21230%2F21%3A00355080" target="_blank" >RIV/68407700:21230/21:00355080 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1007/s10773-021-04950-6" target="_blank" >https://doi.org/10.1007/s10773-021-04950-6</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s10773-021-04950-6" target="_blank" >10.1007/s10773-021-04950-6</a>

Result language
angličtina
Original language name
Quantum Logics that are Symmetric-difference-closed
Original language description
In this note we contribute to the recently developing study of "almost Boolean" quantum logics (i.e. to the study of orthomodular partially ordered sets that are naturally endowed with a symmetric difference). We call them enriched quantum logics (EQLs). We first consider set-representable EQLs. We disprove a natural conjecture on compatibility in EQLs. Then we discuss the possibility of extending states and prove an extension result for Z(2)-states on EQLs. In the second part we pass to general orthoposets with a symmetric difference (GEQLs). We show that a simplex can be a state space of a GEQL that has an arbitrarily high degree of noncompatibility. Finally, we find an appropriate definition of a "parametrization" as a mapping between GEQLs that preserves the set-representation.
Czech name
—
Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10101 - Pure mathematics

Project
<a href="/en/project/GF20-09869L" target="_blank" >GF20-09869L: The many facets of orthomodularity</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2021
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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