Approximate quantum error correction, eigenstate thermalization and the chaos bound

TL;DR

This paper links quantum error correction, thermalization, and chaos in many-body systems satisfying ETH, showing how chaos bounds limit information preservation and error correction capabilities.

Contribution

It establishes a quantitative connection between chaos bounds, thermalization, and quantum error correction in ETH systems, revealing fundamental limits.

Findings

Chaos bound constrains quantum error correction error

Derived bounds on dynamical fluctuations and fluctuation-dissipation relations

Showed how chaos limits information preservation in thermalizing systems

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.