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

• URL: http://arxiv.org/abs/2412.12279v1
• Date: Mon, 16 Dec 2024 19:00:20 GMT
• Title: Coherent information as a mixed-state topological order parameter of fermions
• Authors: Ze-Min Huang, Luis Colmenarez, Markus Müller, Sebastian Diehl,
• Abstract summary: A quantum memory in the error correctable phase is captured by the presence of a Majorana zero mode. 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.
• Score: 1.351813974961217
• License:
• 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.

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