Entanglement wedge cross sections require tripartite entanglement
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13130_2020_Article_12932.pdf
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Author(s)
Akers, Chris
Rath, Pratik
Date Issued
April 30, 2020
Publisher
Springer Berlin Heidelberg
Citation
Journal of High Energy Physics. 2020 Apr 30;2020(4):208
Version
Final published version
Abstract
Abstract
We argue that holographic CFT states require a large amount of tripartite entanglement, in contrast to the conjecture that their entanglement is mostly bipartite. Our evidence is that this mostly-bipartite conjecture is in sharp conflict with two well- supported conjectures about the entanglement wedge cross section surface EW. If EW is related to either the CFT’s reflected entropy or its entanglement of purification, then those quantities can differ from the mutual information at O1GN.$$ O\left(\frac{1}{G_N}\right). $$ We prove that this implies holographic CFT states must have O1GN.$$ O\left(\frac{1}{G_N}\right). $$ amounts of tripartite entanglement. This proof involves a new Fannes-type inequality for the reflected entropy, which itself has many interesting applications.
MIT Department
Massachusetts Institute of Technology. Center for Theoretical Physics
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Creative Commons Attribution
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DOI of Published Version
https://doi.org/10.1007/JHEP04(2020)208
