Quantum Error Correction in the Black Hole Interior
arXiv:2203.01961 · doi:10.1007/JHEP07(2023)189
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 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.
arXiv comment48+5 pages, 10 figures
References in corpus (42)
- A Covariant Holographic Entanglement Entropy Proposal
- Generalized gravitational entropy
- The Stretched Horizon and Black Hole Complementarity
- Replica Wormholes and the Entropy of Hawking Radiation
- Quantum Extremal Surfaces: Holographic Entanglement Entropy beyond the Classical Regime
- Quantum corrections to holographic entanglement entropy
- Holographic quantum error-correcting codes: Toy models for the bulk/boundary correspondence
- The entropy of bulk quantum fields and the entanglement wedge of an evaporating black hole
- Bulk Locality and Quantum Error Correction in AdS/CFT
- Quantum data processing and error correction
- Reconstruction of Bulk Operators within the Entanglement Wedge in Gauge-Gravity Duality
- Holographic representation of local bulk operators
- The Ryu-Takayanagi Formula from Quantum Error Correction
- State-Dependent Bulk-Boundary Maps and Black Hole Complementarity
- Information Transfer with a Gravitating Bath
- Quantum Computation vs. Firewalls
- Inconsistency of Islands in Theories with Long-Range Gravity
- Black Hole Entanglement and Quantum Error Correction
- What Do CFTs Tell Us About Anti-de Sitter Spacetimes?
- Pulling Out the Island with Modular Flow
- Learning the Alpha-bits of Black Holes
- Leading order corrections to the quantum extremal surface prescription
- Geometric secret sharing in a model of Hawking radiation
- Entanglement between two disjoint universes
- From Euclidean Sources to Lorentzian Spacetimes in Holographic Conformal Field Theories
- Quantum minimal surfaces from quantum error correction
- Quantum algorithm for Petz recovery channels and pretty good measurements
- Quantum Error Correction of Observables
- A World without Pythons would be so Simple
- The ghost in the radiation: Robust encodings of the black hole interior
- Complexity Growth in Integrable and Chaotic Models
- Entanglement in De Sitter Space
- An effective matrix model for dynamical end of the world branes in Jackiw-Teitelboim gravity
- Algebraic and information-theoretic conditions for operator quantum error-correction
- Finding Pythons in Unexpected Places
- Islands in Closed and Open Universes
- Approximate Quantum Error Correction Revisited: Introducing the Alpha-bit
- Approximate quantum error correction
- The Multiverse in an Inverted Island
- Python's Lunches in Jackiw-Teitelboim gravity with matter
- Petz map and Python's lunch
- Operator quantum error correction