A Noisy Approach to Intrinsically Mixed-State Topological Order Ramanjit Sohal and Abhinav Prem propose a framework for studying two-dimensional topologically ordered states under local correlated errors, showing that the resulting mixed-state can exhibit intrinsically mixed-state topological order (imTO), a form of topological order not expected in the ground state of 2D local gapped Hamiltonians. Decoherence, previously interpreted as anyon condensation, is shown to correspond to "gauging out" anyons in the original Hilbert space. This process results in imTO, which is strongly symmetric under certain anomalous 1-form symmetries. The framework connects decohered density matrices to topological subsystem codes, which can appear as anomalous surface states of 3D topological orders. Examples show that the decohered state can host classical or quantum memories, and even chiral or non-modular topological order. The authors argue that decohered states represent genuine mixed-state quantum phases of matter, and that imTO can be partially classified in terms of braided fusion categories. The paper discusses the connection between decoherence and topological subsystem codes (TSSCs), which can describe non-modular and chiral topological orders. It shows that Abelian topological orders can serve as resource states for preparing anomalous topological phases under local quantum channels. The framework maps the decohered density matrix to a vector in a doubled Hilbert space, where decoherence induces anyon condensation. This process corresponds to gauging out anyons in the original Hilbert space, leading to imTO. The authors demonstrate that this process can result in mixed-state quantum phases with zero correlation length and robustness against local noise. They also show that the resulting states can encode logical qubits and support non-trivial braiding statistics. The paper provides examples of imTO, including the Z₂(0) and Z₂(1) TSSCs from the Z₂ Toric code, and the Z₄(1) TSSC from the Z₄ Toric code. These examples illustrate how decoherence can lead to mixed-state topological orders with distinct properties from pure topological states. The authors conclude that imTO can be partially classified in terms of braided fusion categories and that the framework provides a physical mechanism for realizing such codes through local correlated noise.A Noisy Approach to Intrinsically Mixed-State Topological Order Ramanjit Sohal and Abhinav Prem propose a framework for studying two-dimensional topologically ordered states under local correlated errors, showing that the resulting mixed-state can exhibit intrinsically mixed-state topological order (imTO), a form of topological order not expected in the ground state of 2D local gapped Hamiltonians. Decoherence, previously interpreted as anyon condensation, is shown to correspond to "gauging out" anyons in the original Hilbert space. This process results in imTO, which is strongly symmetric under certain anomalous 1-form symmetries. The framework connects decohered density matrices to topological subsystem codes, which can appear as anomalous surface states of 3D topological orders. Examples show that the decohered state can host classical or quantum memories, and even chiral or non-modular topological order. The authors argue that decohered states represent genuine mixed-state quantum phases of matter, and that imTO can be partially classified in terms of braided fusion categories. The paper discusses the connection between decoherence and topological subsystem codes (TSSCs), which can describe non-modular and chiral topological orders. It shows that Abelian topological orders can serve as resource states for preparing anomalous topological phases under local quantum channels. The framework maps the decohered density matrix to a vector in a doubled Hilbert space, where decoherence induces anyon condensation. This process corresponds to gauging out anyons in the original Hilbert space, leading to imTO. The authors demonstrate that this process can result in mixed-state quantum phases with zero correlation length and robustness against local noise. They also show that the resulting states can encode logical qubits and support non-trivial braiding statistics. The paper provides examples of imTO, including the Z₂(0) and Z₂(1) TSSCs from the Z₂ Toric code, and the Z₄(1) TSSC from the Z₄ Toric code. These examples illustrate how decoherence can lead to mixed-state topological orders with distinct properties from pure topological states. The authors conclude that imTO can be partially classified in terms of braided fusion categories and that the framework provides a physical mechanism for realizing such codes through local correlated noise.