Empirically Equivalent Distributions in Ontological Models of Quantum Mechanics

TL;DR

This paper explores the limitations of knowledge in quantum mechanics by showing that certain distributions over ontic states are empirically indistinguishable, implying fundamental constraints on what can be known.

Contribution

It demonstrates that in ontological models of quantum systems, the set of preparable distributions must contain empirically equivalent distributions, revealing inherent limits to empirical knowledge.

Findings

Empirically indistinguishable distributions exist in ontological models.

Not all probability distributions over ontic states are preparable.

There are fundamental limits to what facts in nature can be empirically discovered.

Abstract

We consider ontological models of a quantum system, assuming that not all probability distributions over the space $\Lambda$ of ontic states are preparable, only those belonging to a certain set C. We assume further that every POVM with a finite value space can be measured and that for every density matrix there exists a distribution in C whose outcome statistics is given by the density matrix. We show that this mapping from C to the set of density matrices must be many-to-one, that is, that there must be empirically indistinguishable distributions in C. This shows that there must be limitations to knowledge in the sense of facts in nature that cannot be discovered empirically.