Quantum thermalization achieves optimal approximate quantum error correction

@misc{venkatesh2026quantum,
  title = {{Quantum thermalization achieves optimal approximate quantum error correction}},
  author = {Aditi Venkatesh and Richard R. Allen and Saúl Pilatowsky-Cameo and Bingtian Ye and Soonwon Choi},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.04121},
  eprint = {2609.04121},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.04121},
}

TY  - UNPB
TI  - Quantum thermalization achieves optimal approximate quantum error correction
AU  - Aditi Venkatesh
AU  - Richard R. Allen
AU  - Saúl Pilatowsky-Cameo
AU  - Bingtian Ye
AU  - Soonwon Choi
PY  - 2026
DA  - 2026/09/03
PB  - arXiv
DO  - 10.48550/arxiv.2609.04121
UR  - https://arxiv.org/abs/2609.04121
AB  - Quantum thermalization explains how an isolated many-body system naturally evolves towards a thermal state, rendering information about the initial conditions inaccessible to local measurements. This is precisely the mechanism utilized in quantum error correction, where information is protected by design through a nonlocal encoding. In this work, we leverage this connection to port the rigorous framework of (approximate) quantum error correction to the study of quantum thermalization. Treating typical late-time states as codewords, we characterize the error-correcting properties of generic thermalizing dynamics. We numerically uncover a universal relationship between the encoding rate, distance, and thermal entropy density of the emergent code. At infinite temperature, this universal curve saturates the quantum Singleton bound, achieving the same optimal limit as Haar-random codes. At finite temperature, we introduce a code family based on the Scrooge ensemble, the natural thermal analogue of the Haar ensemble, and prove it saturates the entropic quantum Singleton bound, establishing this family as optimal within entropic constraints. Our extracted universal curve independently saturates this same bound, revealing that finite-temperature thermalization is itself optimal. Finally, we show how conserved quantities limit the error-correcting behavior of thermalization: codewords with differing energies, or other conserved charges, leak only classical information, and correctability persists until the difference reaches the scale of thermal fluctuations. Our results reveal a universal optimal coding structure in thermalizing dynamics, while introducing new optimal codes that achieve fundamental limits of approximate quantum error correction.
ER  -