Linear orthogonality spaces as a new approach to quantum logic
| Authors | |
|---|---|
| Year of publication | 2021 |
| Type | Article in Proceedings |
| Conference | 2021 IEEE International Symposium on Multiple-Valued Logic (ISMVL 2021) |
| MU Faculty or unit | |
| 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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