Transition probability spaces
Johan G. F. Belinfante · Journal of Mathematical Physics · 1976
The set of pure quantum states is described as an abstract space with a geometry determined by transition probabilities. We describe all possible structures for three-dimensional transition probability spaces with less than ten states, as well as some even larger spaces of a certain symmetric type. It is shown that the orthoclosed subspaces of a transition probability space form an atomistic orthomodular poset.