Entanglement wedge cross sections require tripartite entanglement

Journal Article · Thu Apr 30 00:00:00 EDT 2020 · Journal of High Energy Physics (Online)

DOI:https://doi.org/10.1007/jhep04(2020)208· OSTI ID:1658857

Akers, Chris ^[1]; Rath, Pratik ^[2]

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1. Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States); LBNL
2. Univ. of California, Berkeley, CA (United States); Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)

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 wellsupported 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 O(1/G_N). We prove that this implies holographic CFT states must have O(1/G_N) amounts of tripartite entanglement. This proof involves a new Fannes-type inequality for the reflected entropy, which itself has many interesting applications.

• Research Organization: Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States)
• Sponsoring Organization: National Science Foundation (NSF); USDOE Office of Science (SC), High Energy Physics (HEP)
• Grant/Contract Number: AC02-05CH11231; SC0018944; SC0019127; SC0019380
• OSTI ID: 1658857
• Alternate ID(s): OSTI ID: 1693412
• Journal Information: Journal of High Energy Physics (Online), Journal Name: Journal of High Energy Physics (Online) Journal Issue: 4 Vol. 2020; ISSN 1029-8479
• Publisher: Springer Berlin
• Country of Publication: United States
• Language: English

Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
AdS-CFT Correspondence
Gauge-gravity correspondence