Underlining some limitations of the statistical formalism in quantum mechanics: Reply to the Comment of Bodor and Di\'osi

TL;DR

This paper clarifies the limitations of density matrices in quantum mechanics, emphasizing they lack information about ensemble preparation, and responds to critiques by Bodor and Diási to refine this understanding.

Contribution

It highlights the incomplete nature of density matrices in representing quantum ensembles, especially regarding preparation details, and addresses criticisms to clarify this limitation.

Findings

Density matrices do not fully describe quantum ensembles.

Preparation information is not captured by density matrices.

The discussion clarifies the scope of density matrices in quantum theory.

Abstract

In a paper of us, it is showed that Density Matrices do not provide a complete description of ensembles of states in quantum mechanics, since they lack measurable information concerning the preparation of the ensembles. Bodor and Di\'osi have later posted a comment on that article, which agrees on some points of it but disagrees on some others. This reply is intended to clarify the discussion.