Reflected entropy in random tensor networks. Part III. Triway cuts

Akers, Chris; Faulkner, Thomas; Lin, Simon; Rath, Pratik

doi:10.1007/JHEP12(2024)209

Reflected entropy in random tensor networks. Part III. Triway cuts

Journal Article · Fri Dec 27 00:00:00 EST 2024 · Journal of High Energy Physics

DOI:https://doi.org/10.1007/JHEP12(2024)209· OSTI ID:2999763

Akers, Chris ^[1]; Faulkner, Thomas ^[2]; Lin, Simon ^[3]; ^[4]

Univ. of Colorado, Boulder, CO (United States)
Univ. of Illinois at Urbana-Champaign, IL (United States)
New York Univ. Abu Dhabi (United Arab Emirates)
University of California, Berkeley, CA (United States)

For general random tensor network states at large bond dimension, we prove that the integer Rényi reflected entropies (away from phase transitions) are determined by minimal triway cuts through the network. This generalizes the minimal cut description of bipartite entanglement for these states. A natural extrapolation away from integer Rényi parameters, suggested by the triway cut problem, implies the holographic conjecture S_R = 2EW, where S_R is the reflected entropy and EW is the entanglement wedge cross-section. Minimal triway cuts can be formulated as integer programs which cannot be relaxed to find a dual maximal flow/bit-thread description. This sheds light on the gap between the existence of tripartite entanglement in holographic states and the bipartite entanglement structure motivated by bit-threads. In particular, we prove that the Markov gap that measures tripartite entanglement is lower bounded by the integrality gap of the integer program that computes the triway cut.

View Accepted Manuscript (DOE)

Research Organization:: University of California, Berkeley, CA (United States)

Sponsoring Organization:: USDOE Office of Science (SC), High Energy Physics (HEP)

Grant/Contract Number:: AC02-05CH11231; SC0019380

OSTI ID:: 2999763

Journal Information:: Journal of High Energy Physics, Journal Name: Journal of High Energy Physics Journal Issue: 12 Vol. 2024; ISSN 1029-8479

Publisher:: Springer Science and Business Media LLCCopyright Statement

Country of Publication:: United States

Language:: English

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