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Quantum Software Tools Programming

Indistinguishability in general probabilistic theories

arXiv
Authors: John H. Selby, Victoria J. Wright, Máté Farkas, Marcin Karczewski, Ana Belén Sainz

Year

2024

Paper ID

325

Status

Preprint

Abstract Read

~2 min

Abstract Words

109

Citations

N/A

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.

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  • This paper contributes to the Quantum Software Tools & Programming research area in the Quantum Articles archive.
  • It adds a 2024 reference point for readers tracking recent quantum research.
  • The existence of indistinguishable quantum particles provides an explanation for various physical phenomena we observe in nature.

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References & Citation Signals

[1] DOI https://doi.org/arXiv:2412.20963 [2] arXiv https://arxiv.org/abs/2412.20963 [3] Publisher https://arxiv.org/abs/2412.20963

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