Dissipative phase transitions and passive error correction

Understand

We classify different ways to passively protect classical and quantum information, i.e.

• we do not allow for syndrome measurements, in the context of local Lindblad models for spin systems.
• Within this family of models, we suggest that passive error correction is associated with nontrivial phases of matter and propose a definition for dissipative phases based on robust steady state degeneracy of a Lindbladian in the thermodynamic limit.
• We study three thermalizing models in this context: the 2D Ising model, the 2D toric code, and the 4D toric code.