Mixed state topological order: operator algebraic approach

Understand

We study the classification problem of mixed states in two-dimensional quantum spin systems in the operator algebraic framework of quantum statistical mechanics.

• We associate a braided $C^*$-tensor category to each state satisfying a mixed-state version of the approximate Haag duality.
• We study how this category behaves under decoherence: suppose the state is acted by a finite depth quantum channel.
• We prove that the braided $C^*$-tensor category of the final state is a braided $C^*$-tensor subcategory of the initial state.