Eigenstate thermalization hypothesis and approximate quantum error correction

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.

Diagnosing entanglement dynamics in noisy and disordered spin chains via the measurement-induced steady-state entanglement transition

“…Moreover, the obtained value of ν is close to the exponents found for models with completely random stochastic unitary evolution pro-tocols [32], where ν ≈ 0.70 (1) for continuous measurements and ν ≈ 0.80(3) for stroboscopic weak measurements. Notably, these estimates differ significantly from the critical exponent found in a model with stroboscopic projective measurements, where ν ≈ 1.2(2) for Haar unitary evolution and ν ≈ 1.24 (7) for stabilizer circuits [24]. This indicates that the entanglement transition induced by continuous measurements displays a large degree of universality, with all relevant features captured by the single parameter λ c , and further supports our suggestion that this parameter provides reliable insights into the detailed entanglement dynamics of specific physical systems.…”

“…Despite the reversible nature of unitary dynamics, closed many-body quantum systems can exhibit the hallmarks of thermalization. This apparent paradox is explained by the eigenstate thermalization hypothesis (ETH), stating that local observables of generic many-body systems exhibit ergodic dynamics after a finite time [1][2][3][4][5][6][7][8][9][10]. The ergodic regime supports nearmaximal entanglement between different parts of the system, which results in an extensive scaling of the entanglement entropy, known as the volume law.…”

Extended eigenstate thermalization and the role of FZZT branes in the Schwarzian theory

“…It would be very interesting to investigate what more can be said about the properties of the AQECC hosted by the eigenstates of SYK-like models in the light of the OTOC version of ETH we found. Recent investigations linking ETH to AQECC in chaotic theories, including holographic ones, have appeared in [94], while [95] link complexity of time evolution to ETH-type behavior.…”

Complexity and emergence of warped AdS3 space-time from chiral Liouville action

“…The same result still could be applied for WCFTs where we posses a "warped Weyl" symmetry. Specifically, the level of the energy of the dual of these operators in terms of the eigenstate thermalization hypothesis (ETH) [77] have been studied, which could be repeated for WCFTs. One then could check whether for WCFTs the gates would satisfy the ETH ansatz.…”