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@ARTICLE{Huang:1038540,
      author       = {Huang, Ze-Min and Colmenarez, Luis and Müller, Markus and
                      Diehl, Sebastian},
      title        = {{C}oherent information as a mixed-state topological order
                      parameter of fermions},
      reportid     = {FZJ-2025-01525, arXiv:2412.12279},
      year         = {2025},
      note         = {20 pages, 13+3 figures},
      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.},
      cin          = {PGI-2},
      cid          = {I:(DE-Juel1)PGI-2-20110106},
      pnm          = {5221 - Advanced Solid-State Qubits and Qubit Systems
                      (POF4-522)},
      pid          = {G:(DE-HGF)POF4-5221},
      typ          = {PUB:(DE-HGF)25},
      eprint       = {2412.12279},
      howpublished = {arXiv:2412.12279},
      archivePrefix = {arXiv},
      SLACcitation = {$\%\%CITATION$ = $arXiv:2412.12279;\%\%$},
      url          = {https://juser.fz-juelich.de/record/1038540},
}