Linear orthogonality spaces as a new approach to quantum logic
Logic
2021-03-26 v1
Abstract
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 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 .
Cite
@article{arxiv.2103.13764,
title = {Linear orthogonality spaces as a new approach to quantum logic},
author = {Kadir Emir and David Kruml and Jan Paseka and Thomas Vetterlein},
journal= {arXiv preprint arXiv:2103.13764},
year = {2021}
}