A Noisy Approach to Intrinsically Mixed-State Topological Order

Understand

We propose a general framework for studying two-dimensional (2D) topologically ordered states subject to local correlated errors and show that the resulting mixed-state can display intrinsically mixed-state topological order (imTO) -- topological order which is not expected to occur in the ground state of 2D local gapped Hamiltonians.

• Specifically, we show that decoherence, previously interpreted as anyon condensation in a doubled Hilbert space, is more naturally phrased as, and provides a physical mechanism for, ``gauging out" anyons in the original Hilbert space.
• We find that gauging out anyons generically results in imTO, with the decohered mixed-state strongly symmetric under certain anomalous 1-form symmetries.
• This framework lays bare a striking connection between the decohered density matrix and topological subsystem codes, which can appear as anomalous surface states of 3D topological orders.