A derivation of quantum theory from physical requirements

TL;DR

This paper derives the formal structure of quantum theory from five basic physical principles, offering insights into its foundational origins and potential modifications, similar to how special relativity derives spacetime structure.

Contribution

It provides a derivation of quantum formalism from simple physical assumptions, linking mathematical structure to physical principles, and explores possible consistent modifications.

Findings

Derivation of quantum formalism from five physical requirements

Group-theoretic explanation of the Bloch ball's structure

Identification of natural modifications to quantum theory

Abstract

Quantum theory is usually formulated in terms of abstract mathematical postulates, involving Hilbert spaces, state vectors, and unitary operators. In this work, we show that the full formalism of quantum theory can instead be derived from five simple physical requirements, based on elementary assumptions about preparation, transformations and measurements. This is more similar to the usual formulation of special relativity, where two simple physical requirements -- the principles of relativity and light speed invariance -- are used to derive the mathematical structure of Minkowski space-time. Our derivation provides insights into the physical origin of the structure of quantum state spaces (including a group-theoretic explanation of the Bloch ball and its three-dimensionality), and it suggests several natural possibilities to construct consistent modifications of quantum theory.