In this paper, we study the impact of decoherence on the extensive quantum information stored in a ground-state manifold of a chaotic quantum many-body system. The model is a thermofield double (TFD) state of the Sachdev-Ye-Kitaev (SYK) model and its generalizations: By investigating the entanglement between two sides under decoherence, we identify the threshold behavior of the information stored in an extensive ground-state manifold, which also supplies the resource for teleportation and admits a dual description as a two-sided wormhole. We find that under strong fermion-parity–symmetric noise, the mixed state undergoes spontaneous breaking of fermion parity from strong to weak symmetry, which coincides with threshold behavior in the coherent information. Our results highlight the degradation of wormhole traversability in realistic quantum scenarios, as well as providing critical insights into the behavior of approximate constant-rate QEC codes under decoherence.

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• Open quantum systems & decoherence
• Quantum error correction
• Sachdev-Ye-Kitaev model