On the Origin of Linearity and Unitarity in Quantum Theory
Quantum Physics
2026-03-17 v3
Abstract
We reconstruct the transformations of quantum theory using a physically motivated postulate. This postulate states that transformations should be locally applicable, and recovers the linear isometries from pure quantum theory, as well as the completely positive, trace-preserving maps from mixed quantum theory. Notably, in the pure case, linearity with respect to the superposition rule and reversibility are both derived from this locality principle.
Keywords
Cite
@article{arxiv.2305.20063,
title = {On the Origin of Linearity and Unitarity in Quantum Theory},
author = {Matt Wilson and Nick Ormrod},
journal= {arXiv preprint arXiv:2305.20063},
year = {2026}
}