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Topological Quantum Computing

Stacking and the triviality of invertible phases

arXiv
Authors: Sven Bachmann, Alan Getz, Pieter Naaijkens, Naomi Wray

Year

2025

Paper ID

17324

Status

Preprint

Abstract Read

~2 min

Abstract Words

99

Citations

N/A

Abstract

We study the superselection sectors of two quantum lattice systems stacked onto each other in the operator algebraic framework. We show in particular that all irreducible sectors of a stacked system are unitarily equivalent to a product of irreducible sectors of the factors. This naturally leads to a faithful functor between the categories for each system and the category of the stacked system. We construct an intermediate `product' category which we then show is equivalent to the stacked system category. As a consequence, the sectors associated with an invertible state are trivial, namely, invertible states support no anyonic quasi-particles.

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  • This paper contributes to the Topological Quantum Computing research area in the Quantum Articles archive.
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  • We study the superselection sectors of two quantum lattice systems stacked onto each other in the operator algebraic framework.

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References & Citation Signals

[1] DOI https://doi.org/arXiv:2511.08382 [2] arXiv https://arxiv.org/abs/2511.08382 [3] Publisher https://arxiv.org/abs/2511.08382

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