A statistical model for quantum spin and photon number states

The most irreducible way to represent information is a sequence of two symbols. In this paper, we construct quantum states using this basic building block. Specifically, we show that the probabilities that arise in quantum theory can be reduced to counting more fundamental ontic states, which we interpret as event networks and model using sequences of 0's and 1's. A completely self contained formalism is developed for the purpose of organizing and counting these ontic states, which employs the finite cyclic group $\mathbb{Z}_2 = \{0, 1\}$, basic set theory, and combinatorics. This formalism is then used to calculate probability distributions associated with particles of arbitrary spin interacting with sequences of two rotated Stern-Gerlach detectors. These calculations are compared with the predictions of non-relativistic quantum mechanics and shown to deviate slightly. This deviation can be made arbitrarily small and does not lead to violations of relevant no-go theorems, such as Bell's inequalities, the Kochen-Specker theorem, or the PBR theorem. The proposed model is then extended to an optical system involving photon number states passing through a beam splitter. Leveraging recent advancements in high precision experiments on these systems, we then propose a means of testing the new model using a tabletop experiment.