English

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 44 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 33.

Keywords

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}
}
R2 v1 2026-06-24T00:32:59.577Z