Preprint

FZJ-2025-01525

http://join2-wiki.gsi.de/foswiki/pub/Main/Artwork/join2_logo100x88.png Coherent information as a mixed-state topological order parameter of fermions

Huang, Z.-M. ; Colmenarez, L. ; Müller, M. (Corresponding author)FZJ* ; Diehl, S.

2025

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Report No.: arXiv:2412.12279

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.

Note: 20 pages, 13+3 figures

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Contributing Institute(s):

1. Theoretische Nanoelektronik (PGI-2)

Research Program(s):

1. 5221 - Advanced Solid-State Qubits and Qubit Systems (POF4-522) (POF4-522)

Appears in the scientific report 2025

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