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.
Highlights
We continue in this direction by studying the error correcting properties of CFTs in the AdS/CFT correspondence
We explore the properties of eigenstate thermalization hypothesis (ETH) as an error correcting code and show that there exists an explicit universal recovery channel for the code
We show that the theory of universal recovery channels can be applied to the ETH code, and discuss the proposition that all chaotic theories necessarily contain error correcting codes
Summary
Assuming (2.1), one can show that expectation values of local operators match onto thermal expectation values Based on this equivalence, the authors of [20] argue that the ETH density matrix is well-approximated by the reduced density matrix of a global thermal state in the canonical ensemble:. We will assume that the result in [18] that for f < 1/2, all local operators not involving energy conservation obey ETH holds for chaotic CFTs. Let us be careful about what ETH says: ETH does not say that the reduced density matrix of a subregion is exponentially close in trace-distance to a reduced thermal state. When we take the thermodynamic limit, both statements become exact, as expected
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