Strong-to-weak spontaneous symmetry breaking of higher-form non-invertible symmetries in Kitaev's quantum double model

Abstract:Topological orders can be understood as spontaneous symmetry breaking of higher-form symmetries. In the non-abelian case, the broken higher-form symmetries are notably non-invertible. In this work, we extend this framework to mixed states, where symmetries can be either strong or weak. In particular, we investigate the strong-to-weak spontaneous symmetry breaking (SWSSB) of non-invertible higher-form symmetries in non-abelian Kitaev's quantum double models under decoherence. We further show that the resulting decohered quantum double mixed states form a locally indistinguishable set, which also constitutes an information convex set. Importantly, we emphasize that the number of extremal points of this convex set equals the ground-state degeneracy of the corresponding pure state, highlighting that the quantum information encoded in the ground-state subspace is degraded into classical information captured by the convex set of decohered density matrices.

arXiv:2509.24179 [quant-ph]

(or arXiv:2509.24179v3 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2509.24179 Focus to learn more arXiv-issued DOI via DataCite

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