Approximate quantum error correction, eigenstate thermalization and the chaos bound

• URL: http://arxiv.org/abs/2510.26758v1
• Date: Thu, 30 Oct 2025 17:48:57 GMT
• Title: Approximate quantum error correction, eigenstate thermalization and the chaos bound
• Authors: Shozab Qasim, Jason Pollack,
• Abstract summary: We show that chaos bound directly constrains the error of an approximate quantum error-correcting code.<n>Our results reveal how the limits of quantum chaos constrain information preservation in thermalizing quantum systems.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Quantum error correction, thermalization, and quantum chaos are fundamental aspects of quantum many-body physics that have each developed largely independently, despite their deep conceptual overlap. In this work, we establish a precise link between all three in systems that satisfy the eigenstate thermalization hypothesis (ETH) and exhibit a well-defined hierarchy of time scales between dissipation and scrambling. Building on the ETH matrix ansatz and the structure of the out-of-time-order correlator (OTOC), we show that the chaos bound directly constrains the error of an approximate quantum error-correcting code. This establishes a quantitative relation between information scrambling, thermalization, and correctability. Furthermore, we derive bounds on dynamical fluctuations around the infinite-time average and on fluctuation-dissipation relations, expressed in terms of both the code error and the Lyapunov exponent. Our results reveal how the limits of quantum chaos constrain information preservation in thermalizing quantum systems.

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