2013/07/09 by Oscar Dahlsten, Oscar C. O. Dahlsten, Andrew J. P. Garner +8
Computer Science · Mathematics · Physics and Astronomy · #FOS: Physical sciences #Quantum Mechanics and Applications #Quantum Physics (quant-ph) #Topological and Geometric Data Analysis #advanced mathematical theories #quant-ph
paper · pdf · doi:10.48550/arxiv.1307.2529
4 pages + 1 page appendix, 2 figures. Comments welcome
openalex publication_date 2013/07/09 · arxiv created 2013/11/04 · arxiv updated 2013/11/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.