PIRSA:19120050

Entanglement wedge reconstruction and operator algebras

APA

Kang, M. (2019). Entanglement wedge reconstruction and operator algebras. Perimeter Institute. https://pirsa.org/19120050

MLA

Kang, Monica. Entanglement wedge reconstruction and operator algebras. Perimeter Institute, Dec. 10, 2019, https://pirsa.org/19120050

BibTex

          @misc{ pirsa_19120050,
            doi = {},
            url = {https://pirsa.org/19120050},
            author = {Kang, Monica},
            keywords = {Quantum Fields and Strings},
            language = {en},
            title = {Entanglement wedge reconstruction and operator algebras},
            publisher = {Perimeter Institute},
            year = {2019},
            month = {dec},
            note = {PIRSA:19120050 see, \url{https://pirsa.org}}
          }
          

Abstract

In order to satisfy the Reeh-Schlieder theorem, I study the infinite-dimensional Hilbert spaces using von Neumann algebras. I will first present the theorem that the entanglement wedge reconstruction and the equivalence of relative entropies between the boundary and the bulk (JLMS) are exactly identical. Then I will demonstrate the entanglement wedge reconstruction with a tensor network model of von Neumann algebra with type II1 factor, which guarantees the equivalence between the boundary and the bulk. I will further sketch that this toy model can be generalized to provide more general von Neumann algebras, including the case of a type III1 factor. This can give further insights to understanding quantum gravity from an algebraic perspective.