Burau representation, Squier's form, and non-Abelian anyons

Abstract:We study a phase-tunable coherent device that reproduces the matrix-valued braid statistics associated with non-Abelian anyons without assuming pre-existing anyonic quasiparticles. The construction uses the reduced Burau representation, made unitary by Squier's Hermitian form, to implement two noncommuting braid generators on a two-dimensional encoded space. A controlled-order circuit applies the generators in both orders, and optimal single-use discrimination gives a closed-form witness for their order dependence. Together with the braid relation, this certifies the implemented non-Abelian braid action. It does not by itself demonstrate the existence of anyonic quasiparticles.

Quantum Physics (quant-ph); Information Theory (cs.IT); Mathematical Physics (math-ph)

arXiv:2510.18186 [quant-ph]

(or arXiv:2510.18186v5 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2510.18186 Focus to learn more arXiv-issued DOI via DataCite

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