Quantum Error Correction in the Black Hole Interior

TL;DR

This paper models black hole interior quantum error correction using a toy model with Jackiw-Teitelboim gravity, demonstrating robustness of the encoding against generic quantum operations and analyzing error tolerance limits.

Contribution

It introduces a gravitational path integral approach to show the black hole interior's encoding in the radiation is robust against certain quantum errors, with bounds related to black hole entropy.

Findings

Interior density matrix is correctable against specific bath operations

Gravity nearly saturates the Singleton bound for erasure errors

Typical errors must have large rank to corrupt the interior

Abstract

We study the quantum error correction properties of the black hole interior in a toy model for an evaporating black hole: Jackiw-Teitelboim gravity entangled with a non-gravitational bath. After the Page time, the black hole interior degrees of freedom in this system are encoded in the bath Hilbert space. We use the gravitational path integral to show that the interior density matrix is correctable against the action of quantum operations on the bath which (i) do not have prior access to details of the black hole microstates, and (ii) do not have a large, negative coherent information with respect to the maximally mixed state on the bath, with the lower bound controlled by the black hole entropy and code subspace dimension. Thus, the encoding of the black hole interior in the radiation is robust against generic, low-rank quantum operations. For erasure errors, gravity comes within an $O(1)$ distance of saturating the Singleton bound on the tolerance of error correcting codes. For typical errors in the bath to corrupt the interior, they must have a rank that is a large multiple of the bath Hilbert space dimension, with the precise coefficient set by the black hole entropy and code subspace dimension.