Particle exchange in post-quantum theories

TL;DR

This paper explores the possibility of more exotic particle types in post-quantum theories by generalizing exchange statistics measurement, revealing potential for non-abelian particles even in simple 3D space.

Contribution

It introduces a thought experiment to detect exotic particles in post-quantum theories, extending the concept of exchange statistics beyond quantum mechanics.

Findings

Exotic particles can exhibit non-abelian exchange statistics in 3D space.

Witnessing exotic statistics depends on the symmetries allowed in the theory.

Post-quantum scenarios can reveal particles with behaviors beyond quantum bosons and fermions.

Abstract

In quantum theory, particles in three spatial dimensions come in two different types: bosons or fermions, which exhibit sharply contrasting behaviours due to their different exchange statistics. Could more general forms of probabilistic theories admit more exotic types of particles? Here, we propose a thought experiment to identify more exotic particles in general post-quantum theories. We consider how in quantum theory the phase introduced by swapping indistinguishable particles can be measured. We generalise this to post-quantum scenarios whilst imposing indistinguishability and locality principles. We show that our ability to witness exotic particle exchange statistics depends on which symmetries are admitted within a theory. These exotic particles can manifest unusual behaviour, such as non-abelianicity even in topologically simple three-dimensional space.