Coherent information as a mixed-state topological order parameter of fermions

TL;DR

This paper links quantum error correction thresholds in the toric code to topological phase transitions in disordered Majorana fermions, using a mixed-state topological order parameter to measure recoverable quantum information.

Contribution

It introduces a novel connection between quantum error correction phase transitions and topological phases in fermionic systems via a mixed-state topological order parameter.

Findings

Quantum memory stability correlates with Majorana zero modes in vortex defects.

Coherent information acts as a mixed-state topological order parameter.

Error correction threshold corresponds to a topological phase transition in fermions.

Abstract

Quantum error correction protects quantum information against decoherence provided the noise strength remains below a critical threshold. This threshold marks the critical point for the decoding phase transition. Here we connect this transition in the toric code to a topological phase transition in disordered Majorana fermions at high temperatures. A quantum memory in the error correctable phase is captured by the presence of a Majorana zero mode, trapped in vortex defects associated with twisted boundary conditions. These results are established by expressing the coherent information, which measures the amount of recoverable quantum information in a given noisy code, in terms of a mixed-state topological order parameter of fermions. Our work hints at a broader connection of the robustness of quantum information in stabilizer codes and mixed-state topological phase transitions in symmetry protected fermion matter.