# Eigenstate Thermalization Hypothesis and Approximate Quantum Error Correction

## TL;DR

This paper explores the connection between the eigenstate thermalization hypothesis (ETH) and quantum error correction, demonstrating that ETH systems inherently contain error correcting codes, with implications for black hole physics and holography.

## Contribution

It establishes ETH as an error correcting code with a universal recovery channel and extends the framework to chaotic theories and AdS/CFT, highlighting black hole robustness.

## Key findings

- ETH corresponds to an approximate quantum error correcting code.
- Existence of a universal recovery channel for ETH-based codes.
- Black holes exhibit strong error correction properties in holographic models.

## Abstract

The eigenstate thermalization hypothesis (ETH) is a powerful conjecture for understanding how statistical mechanics emerges in a large class of many-body quantum systems. It has also been interpreted in a CFT context, and, in particular, holographic CFTs are expected to satisfy ETH. Recently, it was observed that the ETH condition corresponds to a necessary and sufficient condition for an approximate quantum error correcting code (AQECC), implying the presence of AQECCs in systems satisfying ETH. In this paper, we explore the properties of ETH as an error correcting code and show that there exists an explicit universal recovery channel for the code. Based on the analysis, we discuss a generalization that all chaotic theories contain error correcting codes. We then specialize to AdS/CFT to demonstrate the possibility of total bulk reconstruction in black holes with a well-defined macroscopic geometry. When combined with the existing AdS/CFT error correction story, this shows that black holes are enormously robust against erasure errors.