Publication details

Linear orthogonality spaces as a new approach to quantum logic

Authors

EMIR Kadir KRUML David PASEKA Jan VETTERLEIN Thomas

Year of publication 2021
Type Article in Proceedings
Conference 2021 IEEE International Symposium on Multiple-Valued Logic (ISMVL 2021)
MU Faculty or unit

Faculty of Science

Citation
Web https://ieeexplore.ieee.org/document/9459669
Doi http://dx.doi.org/10.1109/ISMVL51352.2021.00015
Keywords Orthogonality spaces; undirected graphs; linear orthogonality spaces; finite rank
Description 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.
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