Derivation of quantum theory with superselection rules

TL;DR

This paper reconstructs finite-dimensional quantum theory incorporating superselection rules from four operational postulates, clarifying the foundational principles underlying hybrid quantum-classical systems.

Contribution

It introduces a reconstruction of quantum theory with superselection rules based on four purely operational postulates, highlighting the distinctions from classical and fully quantum theories.

Findings

Reconstruction of quantum theory with superselection rules from operational principles

Identification of additional postulates distinguishing classical and quantum theories

Framework for describing hybrid quantum-classical systems

Abstract

We reconstruct finite-dimensional quantum theory with superselection rules, which can describe hybrid quantum-classical systems, from four purely operational postulates: symmetric sharpness, complete mixing, filtering, and local equality. It has been shown that each of the classical and fully quantum theories is singled out by an additional postulate.