Perturbative analysis of topological entanglement entropy from conditional independence

Understand

We use the structure of conditionally independent states to analyze the stability of topological entanglement entropy.

• For the ground state of quantum double or Levin-Wen model, we obtain a bound on the first order perturbation of topological entanglement entropy in terms of its energy gap and subsystem size.
• The bound decreases superpolynomially with the size of the subsystem, provided the energy gap is nonzero.
• We also study the finite temperature stability of stabilizer models, for which we prove a stronger statement than the strong subadditivity of entropy.