Compatibility for Probabilistic Theories
Probabilistic theory (PT), quantum mechanics
We define an index of compatibility for a probabilistic theory (PT). Quantum mechanics with index 0 and classical probability theory with index 1 are at the two extremes. In this way, quantum mechanics is at least as incompatible as any PT. We consider a PT called a concrete quantum logic that may have compatibility index strictly between 0 and 1, but we have not been able to show this yet. Finally, we show that observables in a PT can be represented by positive, vector-valued measures.
Gudder, S. (2013). Compatibility for probabilistic theories. Mathematics Preprint Series. Retrieved from https://digitalcommons.du.edu/math_preprints/23