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Holographic Entanglement of Purification from Conformal Field Theories

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arxiv 1812.05268 v1 pith:57CPMFFV submitted 2018-12-13 hep-th cond-mat.stat-mechquant-ph

Pawel Caputa , Masamichi Miyaji , Tadashi Takayanagi , Koji Umemoto This is my paper · ORCID
classification hep-thcond-mat.stat-mechquant-ph
keywords entanglementholographicpurificationconformalfieldminimalpath-integralpurified
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We explore a conformal field theoretic interpretation of the holographic entanglement of purification, which is defined as the minimal area of entanglement wedge cross section. We argue that in AdS3/CFT2, the holographic entanglement of purification agrees with the entanglement entropy for a purified state, obtained from a special Weyl transformation, called path-integral optimizations. By definition, this special purified state has the minimal path-integral complexity. We confirm this claim in several examples.

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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. Entanglement Wedges from Information Metric in Conformal Field Theories

    hep-th 2019-08 conditional novelty 7.0 of 10

    In holographic CFTs, the Bures information metric of locally excited reduced density matrices vanishes outside the entanglement wedge and matches the AdS time-slice metric inside, giving a CFT-side derivation of wedge...

  2. Phase transitions and uberholography of holographic pure-state geometries

    hep-th 2026-07 conditional novelty 6.0 of 10

    A cross-ratio threshold relation η'/η = e^{ΔH/2} governs entanglement-wedge phase transitions on pure-state holographic geometries, and uberholography's fractal dimension α ≈ 0.786 persists on asymptotic boundaries bu...

  3. Optimal symmetry operators

    hep-th 2025-09 conditional novelty 6.0 of 10

    The Araki cone α=0 purification uniquely attains the Uhlmann fidelity, defining an 'optimal symmetry operator' with maximal expectation value.

  4. A sharp bound on spacetime distance from quantum entanglement

    hep-th 2026-08 conditional novelty 5.0 of 10

    For holographic states, boundary mutual information between regions A and B implies a lower bound on the bulk geodesic distance that grows as log(1/I), forcing divergent separation as I tends to zero.

  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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