Linear orthogonality spaces as a new approach to quantum logic

D 2021

Linear orthogonality spaces as a new approach to quantum logic

EMIR, Kadir; David KRUML; Jan PASEKA and Thomas VETTERLEIN

Basic information

Original name

Linear orthogonality spaces as a new approach to quantum logic

Authors

EMIR, Kadir (792 Turkey, guarantor, belonging to the institution); David KRUML (203 Czech Republic, belonging to the institution); Jan PASEKA (203 Czech Republic, belonging to the institution) and Thomas VETTERLEIN

Edition

Los Alamitos, 2021 IEEE International Symposium on Multiple-Valued Logic (ISMVL 2021), p. 33-38, 6 pp. 2021

Publisher

IEEE Computer Society

Other information

Language

English

Type of outcome

Proceedings paper

Field of Study

10101 Pure mathematics

Country of publisher

United States of America

Confidentiality degree

is not subject to a state or trade secret

Publication form

printed version "print"

References:

URL

RIV identification code

RIV/00216224:14310/21:00119226

Organization unit

Faculty of Science

ISBN

978-1-7281-9225-3

ISSN

DOI

https://doi.org/10.1109/ISMVL51352.2021.00015

UT WoS

000693398200006

EID Scopus

2-s2.0-85113197948

Keywords in English

Orthogonality spaces; undirected graphs; linear orthogonality spaces; finite rank

Abstract

In the original language

The notion of an orthogonality space was recently rediscovered as an effective means to characterise the essential properties of quantum logic. The approach can be considered as minimalistic; solely the aspect of mutual exclusiveness is taken into account. In fact, an orthogonality space is simply a set endowed with a symmetric and irreflexive binary relation. If the rank is at least 4 and if a certain combinatorial condition holds, these relational structures can be shown to give rise in a unique way to Hermitian spaces. In this paper, we focus on the finite case. In particular, we investigate orthogonality spaces of rank at most 3.

Links

GA18-06915S, research and development project

Name: Nové přístupy k agregačním operátorům v analýze a zpracování dat

Investor: Czech Science Foundation

GF20-09869L, research and development project

Name: Ortomodularita z různých pohledů

Investor: Czech Science Foundation, Partner Agency (Austria)

MUNI/G/1211/2017, interní kód MU

Name: Grupové techniky a kvantová informace (Acronym: GRUPIK)

Investor: Masaryk University, INTERDISCIPLINARY - Interdisciplinary research projects

Cite

EMIR, Kadir; David KRUML; Jan PASEKA and Thomas VETTERLEIN. Linear orthogonality spaces as a new approach to quantum logic. In 2021 IEEE International Symposium on Multiple-Valued Logic (ISMVL 2021). Los Alamitos: IEEE Computer Society, 2021, p. 33-38. ISBN 978-1-7281-9225-3. Available from: https://doi.org/10.1109/ISMVL51352.2021.00015.

@inproceedings{1793698,
   author = {Emir, Kadir and Kruml, David and Paseka, Jan and Vetterlein, Thomas},
   address = {Los Alamitos},
   booktitle = {2021 IEEE International Symposium on Multiple-Valued Logic (ISMVL 2021)},
   doi = {https://doi.org/10.1109/ISMVL51352.2021.00015},
   keywords = {Orthogonality spaces; undirected graphs; linear orthogonality spaces; finite rank},
   howpublished = {tištěná verze "print"},
   language = {eng},
   location = {Los Alamitos},
   isbn = {978-1-7281-9225-3},
   pages = {33-38},
   publisher = {IEEE Computer Society},
   title = {Linear orthogonality spaces as a new approach to quantum logic},
   url = {https://ieeexplore.ieee.org/document/9459669},
   year = {2021}
}

TY  - CONF
ID  - 1793698
AU  - Emir, Kadir - Kruml, David - Paseka, Jan - Vetterlein, Thomas
PY  - 2021
TI  - Linear orthogonality spaces as a new approach to quantum logic
PB  - IEEE Computer Society
CY  - Los Alamitos
SN  - 9781728192253
KW  - Orthogonality spaces
KW  - undirected graphs
KW  - linear orthogonality spaces
KW  - finite rank
UR  - https://ieeexplore.ieee.org/document/9459669
N2  - The notion of an orthogonality space was recently rediscovered as an effective means to characterise the essential properties of quantum logic. The approach can be considered as minimalistic; solely the aspect of mutual exclusiveness is taken into account. In fact, an orthogonality space is simply a set endowed with a symmetric and irreflexive binary relation. If the rank is at least 4 and if a certain combinatorial condition holds, these relational structures can be shown to give rise in a unique way to Hermitian spaces. In this paper, we focus on the finite case. In particular, we investigate orthogonality spaces of rank at most 3.
ER  -

EMIR, Kadir; David KRUML; Jan PASEKA and Thomas VETTERLEIN. Linear orthogonality spaces as a new approach to quantum logic. In \textit{2021 IEEE International Symposium on Multiple-Valued Logic (ISMVL 2021)}. Los Alamitos: IEEE Computer Society, 2021, p.~33-38. ISBN~978-1-7281-9225-3. Available from: https://doi.org/10.1109/ISMVL51352.2021.00015.

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