# Quantum sets and Gelfand spectra (Ortho-sets and Gelfand spectra)

@inproceedings{Ding2021QuantumSA, title={Quantum sets and Gelfand spectra (Ortho-sets and Gelfand spectra)}, author={Chun Ding and Chi-Keung Ng}, year={2021} }

Motivated by quantum states with zero transition probability, we introduce the notion of quantum set which is a set equipped with a relation 6=q satisfying: x 6=q y implies both x 6= y and y 6=q x. For a quantum set, a canonical complete ortholattice is constructed. This ortholattice is orthomodular if and only if the quantum set satisfies a canonical condition concerning subsets. This produces a surjective correspondence from the collection of quantum sets to the collection of complete… Expand

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