Stability of topological entanglement entropy under quantum channels in the decohered toric code

Topological entanglement entropy (TEE) is a powerful probe of long-range quantum correlations in pure states, yet its behavior in mixed states remains less well understood. Motivated by this gap, we study the TEE in the decohered toric code, a mixed-state model that exhibits a decodability transition between an uncorrupted phase with a topologically protected quantum memory and a corrupted phase supporting only classical memory. We focus on the two fixed-point limits of this transition—the uncorrupted toric code and the fully decohered toric code—and analyze the response of the TEE when these states are subjected to incoherent local phase-flip noise channels and coherent finite-depth unitary circuits. In both cases, we find that the TEE is perturbatively stable, remaining constant to all orders in perturbation theory in the channel strength. These results support the view that the TEE can serve as a meaningful diagnostic of topological structure even beyond the pure-state setting.