PIRSA:17110136

Video URL

https://pirsa.org/17110136

Approximate Operator Algebra Quantum Error Correction (Decoding the Hologram in AdS/CFT)

Salton, G. (2017). Approximate Operator Algebra Quantum Error Correction (Decoding the Hologram in AdS/CFT). Perimeter Institute for Theoretical Physics. https://pirsa.org/17110136

Salton, Grant. Approximate Operator Algebra Quantum Error Correction (Decoding the Hologram in AdS/CFT). Perimeter Institute for Theoretical Physics, Nov. 22, 2017, https://pirsa.org/17110136 

          @misc{ scivideos_PIRSA:17110136,
            doi = {10.48660/17110136},
            url = {https://pirsa.org/17110136},
            author = {Salton, Grant},
            keywords = {Quantum Information},
            language = {en},
            title = {Approximate Operator Algebra Quantum Error Correction (Decoding the Hologram in AdS/CFT)},
            publisher = {Perimeter Institute for Theoretical Physics},
            year = {2017},
            month = {nov},
            note = {PIRSA:17110136 see, \url{https://scivideos.org/index.php/pirsa/17110136}}
          }

Grant Salton Amazon.com

Talk numberPIRSA:17110136
DOI10.48660/17110136
Source RepositoryPIRSA
Collection
Talk Type Scientific Series
Subject

Abstract

Quantum error correction -- originally invented for quantum computing -- has proven itself useful in a variety of non-computational physical systems, as the ideas of QEC are broadly applicable. In this talk, I'll mention a few examples of error correction in the wild, including the recent discovery that the AdS/CFT correspondence implements quantum error correction.  We will then study the hypothesis that any local bulk operator in AdS can be reconstructed using only a causally disconnected subregion of the CFT.  This hypothesis has been proven under the assumption that error correction in AdS/CFT is exact, but this assumption is not expected to be true.  Fortunately, recent advances in the theory of approximate quantum error correction have emerged.  We will review these results on recoverability and approximate quantum error correction, as well as AdS/CFT and the so-called entanglement wedge reconstruction hypothesis.  We will then prove the entanglement wedge hypothesis robustly and find an explicit formula for reconstructed bulk operators.  If time permits, we will explore a generalization of the theory of universal recovery channels to the case of finite-dimensional von Neumann algebras.