Linear orthogonality spaces as a new approach to quantum logic

2021/03/25 by Emir, Kadir, Kruml, David, Paseka, Jan +1
#05C62 #81P10 #FOS: Mathematics #Logic (math.LO)

paper · doi:10.48550/arxiv.2103.13764

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 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.

Related

• Categories of orthogonality spaces
• Operator Spaces, Linear Logic and the Heisenberg-Schrödinger Duality of Quantum Theory
• Preserver problems for the logics associated to Hilbert spaces and related Grassmannians
• Quantum axiomatics and a theorem of M.P. Soler
• Gradual transitivity in orthogonality spaces of finite rank