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Pré-Publication, Document De Travail Année : 2020

The infinite-dimensional HaPPY code: entanglement wedge reconstruction and dynamics

Résumé

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.

Dates et versions

hal-02739945 , version 1 (02-06-2020)

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Elliott Gesteau, Monica Jinwoo Kang. The infinite-dimensional HaPPY code: entanglement wedge reconstruction and dynamics. 2020. ⟨hal-02739945⟩
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