Why can states and measurement outcomes be represented as vectors?

TL;DR

This paper demonstrates how states and measurement outcomes in quantum and classical systems can be naturally represented as vectors in a real vector space, linking probability data to geometric representations.

Contribution

It introduces a natural vector space representation for states and measurement outcomes from probability data tables, connecting classical and quantum formalisms.

Findings

Vector representations follow naturally from probability data tables.

Properties of the resulting vector sets are analyzed.

Connections with quantum-mechanical formalism are discussed.

Abstract

It is shown how, given a "probability data table" for a quantum or classical system, the representation of states and measurement outcomes as vectors in a real vector space follows in a natural way. Some properties of the resulting sets of these vectors are discussed, as well as some connexions with the quantum-mechanical formalism.