12241 1902.02844 10.1007/JHEP01(2020)168 168 168 Entanglement wedge reconstruction using the Petz map Regular Article - Theoretical Physics 1 14 2020 1 28 2019 11 5 2020 1 8 2020 1 28 The Author(s) 2020 13130 2020 2020 1 1 Chi-Fang Chen chifang@caltech.edu Geoffrey Penington geoffp@stanford.edu Grant Salton gsalton@caltech.edu grid.168010.e 0000000419368956 Department of Physics Stanford University Stanford CA 94305 USA grid.168010.e 0000000419368956 Stanford Institute for Theoretical Physics Stanford University Stanford CA 94305 USA grid.20861.3d 0000000107068890 Institute for Quantum Information and Matter Caltech Pasadena CA 91125 USA Abstract At the heart of recent progress in AdS/CFT is the question of subregion duality, or entanglement wedge reconstruction: which part(s) of the boundary CFT are dual to a given subregion of the bulk? This question can be answered by appealing to the quantum error correcting properties of holography, and it was recently shown that robust bulk (entanglement wedge) reconstruction can be achieved using a universal recovery channel known as the twirled Petz map. In short, one can use the twirled Petz map to recover bulk data from a subset of the boundary. However, this map involves an averaging procedure over bulk and boundary modular time, and hence it can be somewhat intractable to evaluate in practice. We show that a much simpler channel, the Petz map, is sufficient for entanglement wedge reconstruction for any code space of fixed finite dimension — no twirling is required. Moreover, the error in the reconstruction will always be non-perturbatively small. From a quantum information perspective, we prove a general theorem extending the use of the Petz map as a general-purpose recovery channel to subsystem and operator algebra quantum error correction. Keywords AdS-CFT Correspondence 1/N Expansion Nonperturbative Effects ArXiv ePrint: 1902.02844