Coherent information as a mixed-state topological order parameter of fermions
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866912728353865728 |
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| author | Huang, Ze-Min Colmenarez, Luis Müller, Markus Diehl, Sebastian |
| author_facet | Huang, Ze-Min Colmenarez, Luis Müller, Markus Diehl, Sebastian |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_12279 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Coherent information as a mixed-state topological order parameter of fermions Huang, Ze-Min Colmenarez, Luis Müller, Markus Diehl, Sebastian Quantum Physics Disordered Systems and Neural Networks Statistical Mechanics Strongly Correlated Electrons Superconductivity 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. |
| title | Coherent information as a mixed-state topological order parameter of fermions |
| topic | Quantum Physics Disordered Systems and Neural Networks Statistical Mechanics Strongly Correlated Electrons Superconductivity |
| url | https://arxiv.org/abs/2412.12279 |