How to derive quantum formalism from first principles?

TL;DR

This paper proposes a framework to derive quantum formalism from first principles, connecting NPA matrix entries to sequential weak values, but highlights the need for post-selection justification.

Contribution

It links NPA Gamma matrix entries to sequential weak values and explores foundational aspects of deriving quantum theory from basic principles.

Findings

Gamma matrix entries correspond to sequential weak values.

Post-selection is necessary for obtaining sequential weak values.

The framework clarifies the foundational basis of quantum formalism.

Abstract

Suggested a framework to derive the formalism of quantum theory based on the work of Navascues, Pironio and Acin [NJP 10, 073013] (NPA). Specifically, the entries in the Gamma matrices in NPA corrspond to sequential weak values, first analyzed by Mitchison, Popescu and Jozsa [PRA 76, 062105]. However, to obtain the sequential weak values post-selection to the initial state is required, for which we could not find sufficiently strong reason.