On the Origin of Linearity and Unitarity in Quantum Theory

TL;DR

This paper derives the fundamental linear and unitary structure of quantum transformations from a physically motivated locality postulate, unifying pure and mixed quantum theories.

Contribution

It introduces a locality-based postulate that reconstructs quantum transformations, explaining the origin of linearity and unitarity in quantum theory.

Findings

Pure quantum transformations are linear isometries.

Mixed quantum transformations are completely positive, trace-preserving maps.

Linearity and reversibility are derived from the locality principle.

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.