2015/03/20 by Fernando Pastawski, Beni Yoshida, Daniel Harlow +1 · 1 voice · 832 citations
Computer Science · Physics and Astronomy · #Block (permutation group theory) #Boundary (topology) #Degrees of freedom (physics and chemistry) #Hilbert space #Quantum #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum entanglement #Quantum information #Quantum many-body systems #Tensor (intrinsic definition) #hep-th #quant-ph
paper · pdf · doi:10.1007/jhep06(2015)149
published in Journal of High Energy Physics 2015(6) (Springer Nature) · 40 Pages + 25 Pages of Appendices. 38 figures. Typos and bibliographic amendments and minor corrections
arxiv published 2015/03/20 · openalex publication_date 2015/06/01 · arxiv created 2015/07/22 · arxiv updated 2015/07/22 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/06
We propose a family of exactly solvable toy models for the AdS/CFT correspondence based on a novel construction of quantum error-correcting codes with a tensor network structure. Our building block is a special type of tensor with maximal entanglement along any bipartition, which gives rise to an isometry from the bulk Hilbert space to the boundary Hilbert space. The entire tensor network is an encoder for a quantum error-correcting code, where the bulk and boundary degrees of freedom may be identified as logical and physical degrees of freedom respectively. These models capture key features of entanglement in the AdS/CFT correspondence; in particular, the Ryu-Takayanagi formula and the negativity of tripartite information are obeyed exactly in many cases. That bulk logical operators can be represented on multiple boundary regions mimics the Rindlerwedge reconstruction of boundary operators from bulk operators, realizing explicitly the quantum error-correcting features of AdS/CFT recently proposed in [1].