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Petz reconstruction in random tensor networks · Around

2020

Petz reconstruction in random tensor networks

Jia, Hewei Frederic, Rangamani, Mukund

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We illustrate the ideas of bulk reconstruction in the context of random tensor network toy models of holography.

Specifically, we demonstrate how the Petz reconstruction map works to obtain bulk operators from the boundary data by exploiting the replica trick.
We also take the opportunity to comment on the differences between coarse-graining and random projections.

Built on

C.-F. Chen, G. Penington, and G. Salton, Entanglement Wedge Reconstruction using the Petz Map
Original
1902
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G. Penington, S. H. Shenker, D. Stanford, and Z. Yang, Replica wormholes and the black hole interior
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1911
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A. Almheiri, T. Hartman, J. Maldacena, E. Shaghoulian, and A. Tajdini, Replica Wormholes and the Entropy of Hawking Radiation
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1911
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Y. Chen, Pulling Out the Island with Modular Flow
Original
1912
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D. Petz, Sufficient subalgebras and the relative entropy of states of a von Neumann algebra
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A. Hamilton, D. N. Kabat, G. Lifschytz, and D. A. Lowe, Holographic representation of local bulk operators
2006
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S. Ryu and T. Takayanagi, Aspects of Holographic Entanglement Entropy
2006
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V. E. Hubeny, M. Rangamani, and T. Takayanagi, A Covariant holographic entanglement entropy proposal
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2007
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I. Heemskerk, D. Marolf, J. Polchinski, and J. Sully, Bulk and Transhorizon Measurements in AdS/CFT
Original
2012
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Then

P. Hayden, S. Nezami, X.-L. Qi, N. Thomas, M. Walter, and Z. Yang, Holographic duality from random tensor networks
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