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arXiv · 2505.13871

Remarks on orthogonality spaces

John Harding·Remi Salinas Schmeis
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Abstract

We provide two results. The first gives a finite graph constructed from consideration of mutually unbiased bases that occurs as a subgraph of the orthogonality space of $\mathbb{C}^3$ but not of that of $\mathbb{R}^3$. The second is a companion result to the result of Tau and Tserunyan \cite{Tau} that every countable graph occurs as an induced subgraph of the orthogonality space of a Hilbert space. We show that every finite graph occurs as an induced subgraph of the orthogonality space of a finite orthomodular lattice and that every graph occurs as an induced subgraph of the orthogonality space of some atomic orthomodular lattice.

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John Harding, Remi Salinas Schmeis. 2025-05-20. Remarks on orthogonality spaces. https://arxiv.org/abs/2505.13871

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