Derivation of Born Rule from Algebraic and Statistical Axioms

TL;DR

This paper introduces a new axiomatic framework based on algebraic and statistical principles, demonstrating how the Born rule naturally emerges through the concept of sectors in quantum states.

Contribution

It presents a novel axiomatic approach that derives the Born rule from algebraic and statistical axioms using sector theory.

Findings

Born rule derived from axioms

Sectors as key to understanding quantum probabilities

New axiomatic foundation for quantum mechanics

Abstract

In the present paper we propose a new axiomatic system of algebraic and statistical axioms as working hypotheses, from which Born rule can be seen to emerge. In this process the concept of sectors defined as quasi-equivalence classes of factor states plays a crucial role.