Leaks: quantum, classical, intermediate, and more

TL;DR

This paper introduces the concept of leaks in process theories, showing quantum has minimal leakage, classical has maximal, and explores how leaks relate to the emergence of classicality and the definition of purity.

Contribution

It defines leaks in general process theories, constructs a framework for adjoining leaks, and refines the concept of purity to include leaks, bridging quantum and classical theories.

Findings

Quantum theory has minimal leakage.

Classical theory has maximal leakage.

Leaking processes relate to the emergence of classicality.

Abstract

We introduce the notion of a leak for general process theories, and identify quantum theory as a theory with minimal leakage, while classical theory has maximal leakage. We provide a construction that adjoins leaks to theories, an instance of which describes the emergence of classical theory by adjoining decoherence-leaks to quantum theory. Finally, we show that defining a notion of purity for processes in general process theories has to make reference to the leaks of that theory ---a feature missing in standard definitions--- hence, we propose a refined definition and study the resulting notion of purity for quantum, classical and intermediate theories.