From Information Geometry to Quantum Theory

TL;DR

This paper demonstrates how the principles of information geometry can be used to derive the quantum formalism by formalizing key quantum features within an information geometric framework.

Contribution

It introduces a novel information geometric approach to reconstruct the finite-dimensional quantum formalism from elementary quantum features.

Findings

Quantum formalism derived from information geometry

Key quantum features formalized within the geometric framework

Reconstruction of quantum theory from information-theoretic principles

Abstract

In this paper, we show how information geometry, the natural geometry of discrete probability distributions, can be used to derive the quantum formalism. The derivation rests upon three elementary features of quantum phenomena, namely complementarity, measurement simulability, and global gauge invariance. When these features are appropriately formalized within an information geometric framework, and combined with a novel information-theoretic principle, the central features of the finite-dimensional quantum formalism can be reconstructed.