The infinite-dimensional HaPPY code: entanglement wedge reconstruction and dynamics
Abstract
We construct an infinite-dimensional analog of the HaPPY code as a growing series of stabilizer codes defined respective to their Hilbert spaces. The Hilbert spaces are related by isometric maps, which we define explicitly. We construct a Hamiltonian that is compatible with the infinite-dimensional HaPPY code and further study the stabilizer of our code, which has an inherent fractal structure. We use this result to study the dynamics of the code and map a nontrivial bulk Hamiltonian to the boundary. We find that the image of the mapping is scale invariant, but does not create any long-range entanglement in the boundary, therefore failing to reproduce the features of a CFT. This result shows the limits of the HaPPY code as a model of the AdS/CFT correspondence, but also hints that the relevance of quantum error correction in quantum gravity may not be limited to the CFT context.
Cite
@article{arxiv.2005.05971,
title = {The infinite-dimensional HaPPY code: entanglement wedge reconstruction and dynamics},
author = {Elliott Gesteau and Monica Jinwoo Kang},
journal= {arXiv preprint arXiv:2005.05971},
year = {2020}
}
Comments
49 pages+references+appendix, 24 figures, 5 tables