Some Negative Remarks on Operational Approaches to Quantum Theory

TL;DR

This paper critiques operational reconstructions of quantum theory, emphasizing their limitations in revealing the fundamental nature of quantum matter and advocating for deeper understanding through symmetric informationally complete POVMs.

Contribution

It offers a critical perspective on operational approaches and highlights the importance of symmetric informationally complete POVMs for foundational insights.

Findings

Operational reconstructions clarify quantum formalism structure

They do not fully explain the fundamental properties of matter

Symmetric informationally complete POVMs may hold key insights

Abstract

Over the last 10 years there has been an explosion of "operational reconstructions" of quantum theory. This is great stuff: For, through it, we come to see the myriad ways in which the quantum formalism can be chopped into primitives and, through clever toil, brought back together to form a smooth whole. An image comes to mind of a brain-teaser puzzle, all sliding and interlocking pieces. There is no doubt that this is invaluable work, particularly for our understanding of the intricate connections between so many quantum information protocols. But to me, it seems to miss the mark for an ultimate understanding of quantum theory; I am left hungry. I still want to know what strange property of matter forces this formalism upon our information accounting. To play on something Einstein once wrote to Max Born, "The quantum reconstructions are certainly imposing. But an inner voice tells me that they are not yet the real thing. The reconstructions say a lot, but do not really bring us any closer to the secret of the `old one'." In this talk, I hope to expand on these points and convey some sense of why I am fascinated with the problem of the symmetric informationally complete POVMs to an extent greater than axiomatic reconstructions.