Conservation of information and the foundations of quantum mechanics

TL;DR

This paper reviews an information-theoretic approach to quantum mechanics, emphasizing axioms like causality, purity-preservation, and purification, which collectively characterize quantum theory and explain phenomena like entanglement without relying on superposition.

Contribution

It introduces a set of axioms that derive quantum theory from information principles, highlighting the role of the Conservation of Information and purification in the foundations of quantum mechanics.

Findings

Purification captures core quantum features like entanglement.

Axioms of causality and purity-preservation are shared by classical and quantum theories.

The framework provides a complete characterization of finite-dimensional quantum theory.

Abstract

We review a recent approach to the foundations of quantum mechanics inspired by quantum information theory. The approach is based on a general framework, which allows one to address a large class of physical theories which share basic information-theoretic features. We first illustrate two very primitive features, expressed by the axioms of causality and purity-preservation, which are satisfied by both classical and quantum theory. We then discuss the axiom of purification, which expresses a strong version of the Conservation of Information and captures the core of a vast number of protocols in quantum information. Purification is a highly non-classical feature and leads directly to the emergence of entanglement at the purely conceptual level, without any reference to the superposition principle. Supplemented by a few additional requirements, satisfied by classical and quantum theory, it provides a complete axiomatic characterization of quantum theory for finite dimensional systems.