Fractional quantum Hall states under decoherence

We investigate the effect of decoherence on fractional quantum Hall (FQH) fluids and their robustness as topological quantum memories. Specifically, we examine the behavior of Laughlin states under dephasing noise using two complementary approaches: (a) using the model wave function and (b) using the error-field double formalism developed recently. Notably, we identify a critical filling factor $\nu_c = 1/8$ separating two regimes of mixed-state phase transition. Below the critical filling, a Berezinskii-Kosterlitz-Thousless (BKT) transition occurs at finite noise strength, separating the topologically ordered Laughlin phase from a critical phase. This transition is characterized by quantum-information quantities that are non-linear functions of the density matrix. On a torus, in particular, the BKT transition marks the critical decoherence above which the quantum memory encoded in the ground state manifold is degraded. In contrast, above $\nu_c$, the quantum memory is extremely resilient against dephasing noise, with the transition occurring only at infinite noise strength.