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A note on invariants of mixed-state topological order in 2D
Yoshiko Ogata·January 14, 2026
Mathematical Physicscond-mat.stat-mechcond-mat.str-elQuantum Physics
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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.