Towards a classification of mixed-state topological orders in two dimensions

Understand

The classification and characterization of topological phases of matter is well understood for ground states of gapped Hamiltonians that are well isolated from the environment.

• However, decoherence due to interactions with the environment is inevitable -- thus motivating the investigation of topological orders in the context of mixed states.
• Here, we take a step toward classifying mixed-state topological orders in two spatial dimensions by considering their (emergent) generalized symmetries.
• We argue that their 1-form symmetries and the associated anyon theories lead to a partial classification under two-way connectivity by quasi-local quantum channels.