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Holographic quantum error-correcting codes: toy models for the bulk/boundary correspondence

Journal of High Energy Physics volume 2015, Article number: 149 (2015) Cite this article

Abstract

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].

A preprint version of the article is available at ArXiv.

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This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.

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Affiliations

  1. Institute for Quantum Information & Matter and Walter Burke Institute for Theoretical Physics, California Institute of Technology, 1200 E. California Blvd., Pasadena, CA, 91125, USA

    Fernando Pastawski, Beni Yoshida & John Preskill

  2. Princeton Center for Theoretical Science, Princeton University, 400 Jadwin Hall, Princeton, NJ, 08540, USA

    Daniel Harlow

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  1. Fernando Pastawski
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  2. Beni Yoshida
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  3. Daniel Harlow
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  4. John Preskill
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Correspondence to Fernando Pastawski.

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ArXiv ePrint: 1503.06237

These authors contributed equally to this work (Fernando Pastawski and Beni Yoshida).

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Pastawski, F., Yoshida, B., Harlow, D. et al. Holographic quantum error-correcting codes: toy models for the bulk/boundary correspondence. J. High Energ. Phys. 2015, 149 (2015). https://doi.org/10.1007/JHEP06(2015)149

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Keywords

  • AdS-CFT Correspondence
  • Lattice Integrable Models