How statistical are quantum states?

TL;DR

This paper introduces a new no-go theorem that limits how well -epistemic interpretations can explain quantum state overlaps, showing that in large Hilbert spaces, only half of the overlap can be attributed to ignorance about underlying states.

Contribution

It presents a novel no-go theorem applicable to any Hilbert space of dimension greater than two, without requiring additional assumptions like locality or non-contextuality.

Findings

In large Hilbert spaces, at most half of the quantum state overlap can be explained by ignorance.

The theorem applies broadly without extra assumptions such as locality or invasiveness.

It constrains -epistemic models in explaining quantum overlaps.

Abstract

A novel no-go theorem is presented which sets a bound upon the extent to which '\Psi-epistemic' interpretations of quantum theory are able to explain the overlap between non-orthogonal quantum states in terms of an experimenter's ignorance of an underlying state of reality. The theorem applies to any Hilbert space of dimension greater than two. In the limit of large Hilbert spaces, no more than half of the overlap between quantum states can be accounted for. Unlike other recent no-go theorems no additional assumptions, such as forms of locality, invasiveness, or non-contextuality, are required.