![]() ![]() ![]() Van Raamsdonk, The Gravity Dual of a Density Matrix, Class. ![]() Rangamani, Causal Holographic Information, JHEP 06 (2012) 114. Morrison, Boundary-to-bulk maps for AdS causal wedges and the Reeh-Schlieder property in holography, JHEP 05 (2014) 053. Lowe, Holographic representation of local bulk operators, Phys. Maldacena, The Large N limit of superconformal field theories and supergravity, Int. Berthiaume, Quantum secret sharing, Phys. Pellizzari, Codes for the quantum erasure channel, Phys. Shor, Scheme for reducing decoherence in quantum computer memory, Phys. 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. 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. We consider it under the restriction of the bulk (logical) Hilbert space to a subspace that generally has no tensor factorization into subsystems. 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. The implications of the results for the operator dictionary in the AdS/CFT correspondence are also discussed. Using this result, we show how to systematically construct the decoders of the quantum error-correcting codes against erasure errors. We first show that a class of operators acting on a given bipartite pure state on ℋ A ⊗ ℋ B can shrink its supports on ℋ A ⊗ ℋ B to only ℋ A or ℋ B while keeping its mappings. ![]()
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