Heisenberg Uncertainty Relations as Statistical Invariants

TL;DR

This paper demonstrates that Heisenberg Uncertainty Relations can be expressed solely through transition probabilities, establishing their necessity and sufficiency for quantum models, and characterizes complex and real quantum models.

Contribution

It shows that uncertainty relations are both necessary and sufficient for quantum models based on transition probabilities, and characterizes complex and real quantum models.

Findings

Uncertainty relations are necessary and sufficient for quantum models.

Transition probabilities alone can express Heisenberg Uncertainty Relations.

Characterizations of complex and real quantum models are provided.

Abstract

For a simple set of observables we can express, in terms of transition probabilities alone, the Heisenberg Uncertainty Relations, so that they are proven to be not only necessary, but sufficient too, in order for the given observables to admit a quantum model. Furthermore distinguished characterizations of strictly complex and real quantum models, with some ancillary results, are presented and discussed.