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

          @misc{ pirsa_PIRSA:15080066,
            doi = {10.48660/15080066},
            url = {https://pirsa.org/15080066},
            author = {Pastawski, Fernando},
            keywords = {Quantum Fields and Strings, Quantum Gravity, Quantum Information},
            language = {en},
            title = {Holographic quantum error-correcting codes: Toy models for the bulk/boundary correspondence},
            publisher = {Perimeter Institute},
            year = {2015},
            month = {aug},
            note = {PIRSA:15080066 see, \url{https://pirsa.org}}
          }
          

Abstract

In this talk I will introduce a family of exactly solvable toy models of a holographic correspondence based on a novel construction of quantum error-correcting codes with a tensor network structure. The building block for these models are a special type of tensor with maximal entanglement along any bipartition, which gives rise to an exact isometry from bulk operators to boundary operators. The entire tensor network is 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 holographic correspondence; in particular, the Ryu-Takayanagi formula and the negativity of tripartite information are obeyed exactly in many cases. I will describe how bulk operators may be represented on the boundary regions mimicking the Rindler-wedge reconstruction.