Aspects of approximate quantum error correction in holography

          @misc{ pirsa_PIRSA:18050011,
            doi = {10.48660/18050011},
            url = {https://pirsa.org/18050011},
            author = {Kim, Isaac},
            keywords = {Quantum Information},
            language = {en},
            title = {Aspects of approximate quantum error correction in holography},
            publisher = {Perimeter Institute},
            year = {2018},
            month = {may},
            note = {PIRSA:18050011 see, \url{https://pirsa.org}}
          }
          

Abstract

Several equivalent formulations of quantum error correction condition will be introduced. Subtleties arise

when the error correction conditions hold only approximately. We will discuss an equivalent formulation that is 

robust to the approximation error. One can leverage this tool to derive the existence of approximate quantum

error correcting code at low energy subspace of CFT that reproduces aspects of the holographic quantum error

correcting code. Using the same tool, we observe that two operators with greatly differing complexity approximately

commute in an appropriate code subspace. This leads to a notion of bulk locality in the entanglement shadow,

but the precise definition of complexity seems to play an important role in determining how well these operators commute

in the subspace.