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Thermal states are vital: Entanglement Wedge Reconstruction from Operator-Pushing

Gesteau, Elliott and Kang, Monica Jinwoo (2020) Thermal states are vital: Entanglement Wedge Reconstruction from Operator-Pushing. . (Unpublished)

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We give a general construction of a setup that verifies bulk reconstruction, conservation of relative entropies, and equality of modular flows between the bulk and the boundary, for infinite-dimensional systems with operator-pushing. In our setup, a bulk-to-boundary map is defined at the level of the C∗-algebras of state-independent observables. We then show that if the boundary dynamics allow for the existence of a KMS state, physically relevant Hilbert spaces and von Neumann algebras can be constructed directly from our framework. Our construction should be seen as a state-dependent construction of the other side of a wormhole and clarifies the meaning of black hole reconstruction claims such as the Papadodimas-Raju proposal. As an illustration, we apply our result to construct a wormhole based on the HaPPY code, which satisfies all properties of entanglement wedge reconstruction.

Item Type:Report or Paper (Discussion Paper)
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Additional Information:The authors are grateful to Ivan Burbano and Matilde Marcolli for discussions and Temple He and Craig Lawrie for helpful comments on this paper. M.J.K. is supported by a Sherman Fairchild Postdoctoral Fellowship. This material is based upon work supported by the U.S. Department of Energy, Office of Science, Office of High Energy Physics, under Award Number DE-SC0011632. E.G. is funded by ENS Paris and would like to thank Matilde Marcolli for her guidance and constant support. Research at Perimeter Institute is supported in part by the Government of Canada through the Department of Innovation, Science and Economic Development Canada and by the Province of Ontario through the Ministry of Colleges and Universities.
Group:Walter Burke Institute for Theoretical Physics
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Department of Energy (DOE)DE-SC0011632
Ontario Ministry of Economic Development and InnovationUNSPECIFIED
Industry CanadaUNSPECIFIED
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Record Number:CaltechAUTHORS:20200521-135605229
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:103380
Deposited By: Joy Painter
Deposited On:21 May 2020 21:04
Last Modified:02 Jun 2023 01:05

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