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Entanglement Wedge Cross Sections Require Tripartite Entanglement

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arxiv 1911.07852 v3 pith:RZPD7XTN submitted 2019-11-18 hep-th quant-ph

Chris Akers , Pratik Rath This is my paper · ORCID
classification hep-thquant-ph
keywords entanglementtripartiteconjecturecrossentropyfracholographicmathcal
verification ladder T0 review T1 audit T2 compute T3 formal
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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 $E_W$. If $E_W$ is related to either the CFT's reflected entropy or its entanglement of purification, then those quantities can differ from the mutual information at $\mathcal{O}(\frac{1}{G_N})$. We prove that this implies holographic CFT states must have $\mathcal{O}(\frac{1}{G_N})$ amounts of tripartite entanglement. This proof involves a new Fannes-type inequality for the reflected entropy, which itself has many interesting applications.

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Cited by 5 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Surviving correlations across a horizon: reflected entropy for bosonic fields in non-inertial frames and black hole spacetimes

    hep-th 2026-08 conditional novelty 6.0 of 10

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  4. Genuine multi-entropy and holography

    hep-th 2025-02 conditional novelty 6.0 of 10

    A new 'genuine multi-entropy' separates true q-party entanglement from lower-party pieces, and holographic systems are shown to carry O(1/G_N) genuine multipartite entanglement for connected regions.

  5. R\'enyi Entanglement of Purification and Half R\'enyi Reflected Entropy in Free Scalar Theory

    hep-th 2025-01 conditional novelty 5.0 of 10

    In a free scalar lattice model, numerical calculations show Rényi entanglement of purification is at least half the Rényi reflected entropy for 0 < n < 2 in the small subsystems tested.

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