Linear orthogonality spaces as a new approach to quantum logic

• Autoři: EMIR Kadir; KRUML David; PASEKA Jan; VETTERLEIN Thomas
• Rok publikování: 2021
• Druh: Článek ve sborníku
• Konference: 2021 IEEE International Symposium on Multiple-Valued Logic (ISMVL 2021)
• Fakulta / Pracoviště MU: Přírodovědecká fakulta
• www: https://ieeexplore.ieee.org/document/9459669
• Doi: http://dx.doi.org/10.1109/ISMVL51352.2021.00015
• Klíčová slova: Orthogonality spaces; undirected graphs; linear orthogonality spaces; finite rank
• Popis: 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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