Indistinguishability in general probabilistic theories

TL;DR

This paper explores the concept of indistinguishable particles within general probabilistic theories, providing frameworks that unify quantum particles like bosons and fermions with broader probabilistic models.

Contribution

It introduces two frameworks for studying indistinguishable particles in GPTs, connecting quantum particle types with general probabilistic models through categorical constructions.

Findings

Recovered bosons and fermions in quantum theory

Unified particle indistinguishability in GPTs

Decomposition of symmetrised state space using category theory

Abstract

The existence of indistinguishable quantum particles provides an explanation for various physical phenomena we observe in nature. We lay out a path for the study of indistinguishable particles in general probabilistic theories (GPTs) via two frameworks: the traditional GPT framework and the diagrammatic framework of process theories. In the first approach we define different types of indistinguishable particle by the orbits of symmetric states under transformations. In the diagrammatic approach, we find a decomposition of the symmetrised state space using two key constructions from category theory: the biproduct completion and the Karoubi envelope. In both cases for pairs of indistinguishable particles in quantum theory we recover bosons and fermions.