The paper "Towards a classification of mixed-state topological orders in two dimensions" by Tyler Ellison and Meng Cheng explores the classification of topological phases of matter in the context of mixed states, where decoherence due to interactions with the environment is inevitable. The authors focus on two-dimensional (2D) systems and investigate their (emergent) generalized symmetries to classify mixed-state topological orders. They argue that 1-form symmetries and associated anyon theories lead to a partial classification under two-way connectivity for quasi-local quantum channels. This allows them to establish mixed-state topological orders that are intrinsically mixed, i.e., those that have no ground state counterpart. The paper provides a wide range of examples, including topological subsystem codes, decohering $G$-graded string-net models, and "classically gauging" symmetry-enriched topological orders. One of the main examples is an Ising string-net model under the influence of dephasing noise. The authors study the resulting space of locally-indistinguishable states and compute modular transformations within a particular coherent space. They identify two possible effects of quasi-local quantum channels on anyon theories: (1) anyons can be incoherently proliferated, reducing to a commutant of the proliferated anyons, or (2) the system can be "classically gauged," resulting in the symmetrization of anyons and an extension by transparent bosons. Based on these mechanisms, the authors conjecture that mixed-state topological orders are classified by premodular anyon theories, where the braiding relations may be degenerate.The paper "Towards a classification of mixed-state topological orders in two dimensions" by Tyler Ellison and Meng Cheng explores the classification of topological phases of matter in the context of mixed states, where decoherence due to interactions with the environment is inevitable. The authors focus on two-dimensional (2D) systems and investigate their (emergent) generalized symmetries to classify mixed-state topological orders. They argue that 1-form symmetries and associated anyon theories lead to a partial classification under two-way connectivity for quasi-local quantum channels. This allows them to establish mixed-state topological orders that are intrinsically mixed, i.e., those that have no ground state counterpart. The paper provides a wide range of examples, including topological subsystem codes, decohering $G$-graded string-net models, and "classically gauging" symmetry-enriched topological orders. One of the main examples is an Ising string-net model under the influence of dephasing noise. The authors study the resulting space of locally-indistinguishable states and compute modular transformations within a particular coherent space. They identify two possible effects of quasi-local quantum channels on anyon theories: (1) anyons can be incoherently proliferated, reducing to a commutant of the proliferated anyons, or (2) the system can be "classically gauged," resulting in the symmetrization of anyons and an extension by transparent bosons. Based on these mechanisms, the authors conjecture that mixed-state topological orders are classified by premodular anyon theories, where the braiding relations may be degenerate.