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Shrinking of operators in quantum error correction and AdS/CFT.
- Source :
-
Journal of High Energy Physics . Dec2019, Vol. 2019 Issue 12, p1-38. 38p. - Publication Year :
- 2019
-
Abstract
- We first show that a class of operators acting on a given bipartite pure state on ℋA ⊗ ℋB can shrink its supports on ℋA ⊗ ℋB to only ℋA or ℋB while keeping its mappings. Using this result, we show how to systematically construct the decoders of the quantum error-correcting codes against erasure errors. The implications of the results for the operator dictionary in the AdS/CFT correspondence are also discussed. The "sub- algebra code with complementary recovery" introduced in the recent work of Harlow is a quantum error-correcting code that shares many common features with the AdS/CFT correspondence. We consider it under the restriction of the bulk (logical) Hilbert space to a subspace that generally has no tensor factorization into subsystems. In this code, the central operators of the reconstructed algebra on the boundary subregion can emerge as a consequence of the restriction of the bulk Hilbert space. Finally, we show a theorem in this code which implies the validity of not only the entanglement wedge reconstruction but also its converse statement with the central operators. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 11266708
- Volume :
- 2019
- Issue :
- 12
- Database :
- Academic Search Index
- Journal :
- Journal of High Energy Physics
- Publication Type :
- Academic Journal
- Accession number :
- 141317180
- Full Text :
- https://doi.org/10.1007/JHEP12(2019)128