A note on invariants of mixed-state topological order in 2D

Yoshiko Ogata

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arXiv · 2601.09909

A note on invariants of mixed-state topological order in 2D

Yoshiko Ogata

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Abstract

The classification of mixed-state topological order requires indices that behave monotonically under finite-depth quantum channels. In two dimensions, a braided $C^*$-tensor category, which corresponds to strong symmetry, arises from a state satisfying approximate Haag duality. In this note, we show that the $S$-matrix and topological twists of the braided $C^*$-tensor category are quantities that are monotone under finite-depth quantum channels.

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Yoshiko Ogata. 2026-01-14. A note on invariants of mixed-state topological order in 2D. https://arxiv.org/abs/2601.09909

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