Faithful orthogonal representations of graphs from partition logics

TL;DR

This paper explores the relationship between graph representations in partition logics and probability models, showing that the structure of observables alone does not determine probability types and that complementarity does not necessarily imply contextuality.

Contribution

It introduces faithful orthogonal representations of graphs from partition logics and analyzes their implications for classical and quantum probability interpretations.

Findings

Probabilities can be derived from orthogonal graph representations.

The structure of observables does not solely determine probability types.

Complementarity does not imply contextuality.

Abstract

The graphs induced by partition logics allow a dual probabilistic interpretation: a classical one for which probabilities lie on the convex hull of the dispersion-free weights, and another one, suggested independently from the quantum Born rule, in which probabilities are formed by the (absolute) square of the inner product of state vectors with the faithful orthogonal representations of the respective graph. Two immediate consequences are the demonstration that the logico-empirical structure of observables does not determine the type of probabilities alone, and that complementarity does not imply contextuality.