Pith. sign in

REVIEW 4 major objections 5 minor 10 cited by

Temporal Entanglement from Holographic Entanglement Entropy

T0 review · 4 major / 5 minor · reviewed 2026-08-06 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

Pith's one-line read A new holographic prescription for timelike entanglement entropy: continue all real extremal surfaces around the light cone through a complex angle, then select the surface with the smallest real area.

desk verdict A plausible and clearly written proposal for holographic timelike entanglement entropy, with a real circularity burden in the core prescription and solid independent support from the analytic cylinder example; worth refereeing. read the letter →

arxiv 2507.17847 v2 pith:4WGPKU5T submitted 2025-07-23 hep-th quant-ph

Michal P. Heller , Fabio Ori , Alexandre Serantes This is my paper
classification hep-thquant-ph MSC 81T3583C5781P42 PACS 04.60.-m03.67.Mn04.70.Dy
keywords timelikeentanglemententropyholographicanalyticcontinuationextremalsurfaceslight-conesingularitiesUV-IRcorrespondenceAdS/CFTcomplexsaddles
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This paper proposes a concrete rule for defining timelike (temporal) entanglement entropy in holographic quantum field theories. The rule starts from the ordinary entanglement entropy of a spatial region and analytically continues it by rotating the region in the time-space plane through a complexified angle that detours around the light cone. In the bulk, this means continuing every real extremal surface that could contribute to holographic entanglement entropy, and then selecting the resulting complex extremal surface with the smallest real part of the area. The authors argue this resolves the earlier ambiguity about which of several complex extremal surfaces dominates, and that it makes the entropy reduce to the vacuum answer for small timelike subregions while producing the singularities expected in two-dimensional CFTs when interval endpoints are null-separated.

What carries the argument

The central object is the complexified rotation path $\theta = \pi/4 - \epsilon e^{i\alpha}$ with $\epsilon \to 0^+$, which moves the entangling region from a spacelike to a timelike orientation while detouring around the null configuration where its proper size vanishes. The ordering rule that carries the argument is: continue all homology-constrained real extremal surfaces across this path, then pick the complex surface whose area has the smallest real part. In the strip setup the underlying mechanism is a branch rearrangement of extremal surfaces near the light cone, with the real vacuum-connected, unstable and horizon-connected branches merging with complex branches, which determines which complex saddle at $\theta = \pi/2$ is reachable from a real entangling surface.

What would settle it

Compute the dominant complex extremal surface for a fixed timelike strip at $\theta = \pi/2$ using a different complexified continuation path, for example approaching the light cone with a different phase or from the other side, and check whether the selected surface and the entropy change; alternatively, evaluate timelike entanglement entropy directly in a free-fermion or tensor-network model of a 2D CFT interval and compare the small-subregion limit and the null-separation singularities with the predictions of the analytic continuation.

Watch

Extended reading notes

Core claim

The paper's central claim is that holographic timelike entanglement entropy is not obtained by minimizing over all complex extremal surfaces anchored on the timelike region; it is obtained by first analytically continuing all real extremal surfaces that obey the homology constraint and contribute to the spacelike entanglement entropy immediately before the region becomes null, and then minimizing the real part of their analytically continued areas. The continuation follows the path $\theta = \pi/4 - \epsilon e^{i\alpha}$ with $\epsilon \to 0^+$ and $\alpha$ running from $0$ to $\pi$, which carries the region around the light-cone singularity. Applied to a strip in a four-dimensional black brane background, this prescription shows that the vacuum-connected branch of complex surfaces descends from the real vacuum-connected entangling surfaces, while the vacuum-disconnected branches descend from unstable and horizon-connected (or from complexified) branches; as a result, for all strip widths at $\theta = \pi/2$ the vacuum-connected branch dominates and the entropy reduces to the vacuum value for small subregions. In the three-dimensional black hole (BTZ) and conical-defect geometries, the same ordering rule---continue first, minimize after---is necessary to reproduce the light-cone singularities of the two-dimensional CFT entanglement entropy, because the saddle that dominates before crossing a null singularity does not in general dominate afterward.

Load-bearing premise

The load-bearing premise is that the specific complexified path chosen to cross the light cone, the one in Eq. (10), is the correct way to resolve the branch structure, an assumption imposed rather than derived because it is the choice that makes small timelike subregions reproduce the vacuum answer.

Editorial extensions

If this is right

  • For a strip in the planar holographic thermal state, the timelike entanglement entropy is always dominated by the vacuum-connected branch of complex extremal surfaces, so the ambiguity left open by the earlier work is resolved.
  • For sufficiently small timelike subregions, the entropy equals the vacuum-state answer, enforcing the UV-IR correspondence by construction.
  • In the two-dimensional CFT on a cylinder, the holographic timelike entanglement entropy exhibits light-cone singularities whenever the interval endpoints are null-separated, including additional kinematic singularities involving the complement, matching the twist-operator expectation.
  • The dominant saddle for the timelike entropy must be chosen after the analytic continuation: minimizing before crossing the light cone would miss the null singularities, so the two operations do not commute.
  • Close to the light cone and for large intervals, the holographic timelike entanglement entropy has a zeroth-order phase transition when the vacuum-disconnected saddles become available, followed by a first-order transition at larger separations.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • The paper's ordering rule, continue first and minimize after, is structurally the same iε rule used for real-time correlation functions; this suggests the prescription may generalize beyond entropy, for instance to Wilson loops, as the authors note, and to other observables defined by extremal surfaces.
  • If timelike entanglement entropy obeys strong subadditivity whenever the real parts of the areas are nonzero, a property the paper states follows from its construction, the quantity may admit a genuine information-theoretic interpretation as a quasientropy, testable in Gaussian lattice models where timelike reduced density matrices can be built directly.
  • The paper's self-consistency lesson that complex extremal surfaces should not be treated as subleading saddles of ordinary holographic entanglement entropy may rule out some proposed complex-saddle corrections in other holographic computations.
  • Replacing the fixed region by intervals that wrap around the cylinder before rotation, as sketched in the outlook, would extend the definition to timelike intervals longer than the cylinder circumference and could be compared with tensor-network temporal entanglement computations.
Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

4 major / 5 minor

Summary. The paper proposes a prescription for defining timelike (temporal) entanglement entropy in relativistic quantum field theory, and implements it holographically. Starting from standard spatial entanglement entropy of a flat subregion on a constant-time slice, the subregion is rotated through a complexified angle around the light cone; in holography, all real codimension-two extremal surfaces satisfying the homology constraint just before the light cone are analytically continued to the timelike regime, and the dominant contribution is the complex saddle with the smallest real part of the area. The prescription is applied to two settings: a strip in an AdS4 black brane dual to a thermal state on R^{1,2}, and intervals on the Lorentzian cylinder R×S^1 dual to AdS3 geometries (vacuum, conical defect, BTZ). The authors find that, in the AdS4 case, the prescription selects the vacuum-connected complex branch for small timelike subregions, thereby enforcing the UV-IR correspondence, while vacuum-disconnected branches become available only above a critical size, leading to zeroth- and first-order phase transitions. In the AdS3 case, the prescription is shown to reproduce the expected null kinematical singularities, provided minimization is performed after analytic continuation across the light cone.

Significance. If the proposed prescription is correct, it resolves the ambiguity among the multiple complex extremal surfaces identified in Ref. [28], giving a concrete holographic definition of timelike entanglement entropy with plausible physical properties: reduction to the vacuum answer for small subregions, light-cone singularities in 2D CFTs, and a definite ordering between saddle selection and analytic continuation. The paper's strongest assets are the closed-form AdS3 cylinder analysis, where geodesic lengths are analytic and the non-commutation of minimization and continuation can be checked directly, and the explicit kinematic-singularity argument in Sec. IV. The authors are also transparent about the status of their proposal, acknowledging in Secs. II.C and III.F that the UV-IR correspondence is used both to select and to validate the prescription. The main weakness is that the central branch-selection rule is a proposal rather than a derivation, and its 4D implementation rests on numerical continuation at finite regulator without a convergence study.

major comments (4)
  1. [Secs. II.B-II.C and III.F] The central selection rule is not derived but fixed by the UV-IR correspondence. The complexified path in Eq. (10) and the instruction to continue all real saddles are chosen so that small timelike subregions reduce to the vacuum answer; Sec. III.F then cites exactly this property ('upholds the UV-IR correspondence by construction') as evidence and draws the additional conclusion that complex extremal surfaces should never act as subleading saddles. This makes the main claim in Sec. III self-validating rather than independently tested. The authors should either derive the continuation rule from an independent principle, such as a required analyticity property of the entropy functional or of the bulk on-shell action, or explicitly present the rule as a conjecture and separate the UV-IR self-consistency condition from the evidence, listing predictions that would falsify it.
  2. [Sec. III.E and Figs. 6, 8-10, 12] The load-bearing branch assignment is established only numerically. The claim that vacuum-disconnected branches are excluded for Δr<Δr*_min and become available for Δr≥Δr*_min is central to the zeroth-order transition in Sec. III.F, but it relies on continuation at finite ε=10^-4, resolution of the collision at θ⋆ by taking Im θ→0^-, power-law fits in Fig. 6 with no error bars, and numerically extrapolated curves in Fig. 12. Without a systematic ε-scan with error estimates, or an analytic argument that the pairing is ε-independent in the limit ε→0^+, the reader cannot assess whether the phase structure is a genuine consequence of the prescription or an artifact of the numerical resolution. Please provide convergence data for zt,max, Δrmin, and the branch trajectories over several decades of ε, or a proof of ε-independence of the branch assignment.
  3. [Eq. (10) and Sec. III.D] The outcome of the prescription depends on the chosen complex detour, in particular on the sign of Im(θ) while crossing the light cone. The branch rearrangement listed in Sec. III.D is stated for Im(θ)→0^-, and there is no demonstration that the opposite side of the light cone or a different contour that avoids the null singularity would give the same set of contributing saddles. Since the physical content of the proposal is precisely which complex saddle dominates, the prescription requires either a proof of path independence or a physical argument for the chosen sign of Im(θ); otherwise the rule 'select the saddle with smallest Re Areg after continuation' is not well defined in the timelike regime.
  4. [Sec. IV.C] The AdS3 argument that minimization must be performed after analytic continuation is supported by Figs. 15-17 and the limit in Eq. (18), but the key statement that the configuration exhibiting the kinematical divergence always dominates after continuation is asserted rather than proved ('From this kind of limits it is always possible to show...'). Because this is the independent two-dimensional evidence for the ordering prescription, a concise argument covering all windings n and all three singularities θ1, θ2, θ3 would considerably strengthen the paper; without it, the null-singularity test remains a numerical example rather than a general consistency proof.
minor comments (5)
  1. [Abstract] The phrase 'Our prescriptions starts' contains a subject-verb agreement error and should read 'Our prescription starts'.
  2. [Sec. V] The Outlook refers to 'the two-dimensional conformal field theory setup on a Lorentzian cylinder considered in Sec. III', but that setup is analyzed in Sec. IV.
  3. [Sec. IV.C] The sentence 'in Sec. V we will speculate on how to beyond Δr=2π' is ungrammatical; it should read 'how to go beyond Δr=2π'.
  4. [Sec. II.B and Fig. 6] The paper does not state whether the numerical code or data underlying Figs. 6-12 will be made available; given that several claims depend on extrapolated numerical curves, a data availability statement or repository would improve reproducibility.
  5. [Sec. V] The statement that the minimization aspect 'leads to strong subadditivity of holographic timelike entanglement entropy provided the real part of all involved surfaces is nonzero' is given without derivation or reference; either a short argument or a caveat that this is a conjecture should be added.

Circularity Check

1 steps flagged · score 6.0 of 10

UV-IR correspondence is both the stated guiding principle and the reported output ('by construction') of the branch-selection prescription; partial circularity.

  1. self definitional [Secs. II C and III F (paragraph after Fig. 11)]
    "Our guiding principle is that the quantity we define holographically respects the UV-IR correspondence [34]. In particular, the key self-consistency condition will be for us that for sufficiently small temporal subregions in general excited states the quantity they give rise to reduces to the vacuum state answer."

    The UV-IR correspondence is introduced as the guiding principle and key self-consistency condition that selects the prescription: small temporal subregions must reduce to the vacuum answer. In Sec. III F the same property is reported as the successful output of the prescription and is explicitly described as holding 'by construction.' The branch-selection rule (continue only the real extremal surfaces present immediately before the light cone, then minimize Re A after continuation) was adopted precisely so that this condition would hold, and the alternative of minimizing over all complex surfaces is rejected because it would violate UV-IR. Therefore the Sec.

full rationale

The main circularity burden is explicit and localizable: the paper states that UV-IR correspondence is the guiding principle and key self-consistency condition, then in Sec. III F reports that the timelike entanglement entropy 'upholds the UV–IR correspondence by construction.' The small-subregion vacuum reduction, which is the central physical content of the Sec. III branch selection, is therefore an input condition rather than a derived consequence. No load-bearing self-citation circularity is present: Ref. [28] is prior work by overlapping authors but supplies the geometric classification of complex extremal surfaces as an external, checkable input, not an invoked uniqueness theorem. The 2D cylinder section is genuinely independent in part: the geodesic lengths are closed-form, the analytic continuation can be followed explicitly, and the resulting null singularities are compared with the known CFT twist-operator expectation. That comparison gives the ordering of minimization versus analytic continuation real predictive power and justifies a partial rather than total circularity score. The small-but-finite epsilon numerical extrapolations in the 4D strip are a correctness and robustness concern, not a circularity concern.

Assumptions & free parameters 3 free parameters · 7 assumptions · 0 invented entities

The paper rests on the AdS/CFT dictionary for entanglement entropy, plus several prescription choices (complexified light-cone crossing, minimization after continuation, UV-IR as selection principle) that are not derived from underlying principles. The only numerically calibrated inputs are the near-light-cone scaling exponents and the threshold Delta r*_min.

free parameters (3)
  • epsilon (light-cone regulator) = 10^-4 used in numerics; limit epsilon -> 0+
    Small complex-angle regulator in Eq. (10); chosen small but finite in numerical continuation, with convergence assumed.
  • Power-law exponents for near-light-cone behavior = 1/3 for z_t,max, -1/6 for Delta r_max
    Fitted to numerical data in Fig. 6, not derived from a first-principles argument.
  • Delta r*_min = approximately 10.486 z_H
    Limiting value of Delta r_min(epsilon) as epsilon -> 0, obtained by numerical extrapolation; sets the threshold for vacuum-disconnected saddles to become available.
assumptions (7)
  • standard math AdS/CFT duality and the Ryu-Takayanagi/Hubeny-Rangamani-Takayanagi prescription for holographic entanglement entropy.
    Used throughout to identify entanglement entropy with the area of extremal surfaces (Sec. I, Eq. (3)).
  • domain assumption The homology constraint on bulk extremal surfaces.
    Invoked to select allowed extremal surfaces in both thermal examples (Sec. III B and Sec. IV B).
  • ad hoc to paper Timelike entanglement entropy is defined by analytic continuation of spatial entanglement entropy through a complexified rotation around the light cone.
    This is the core proposal of Sec. II A, not derived from underlying principles.
  • ad hoc to paper Among analytically continued complex extremal surfaces, the leading saddle is the one with smallest real part of the area.
    Stated in Sec. II B as part of the prescription, and used throughout Secs. III and IV.
  • ad hoc to paper All real extremal surfaces contributing to holographic entanglement entropy just before the light cone must be continued, not only the dominant one.
    Central to the prescription; stated in Sec. II B and used to include or exclude branches in Sec. III E.
  • ad hoc to paper The UV-IR correspondence is the correct self-consistency criterion for timelike entanglement entropy.
    Adopted as a guiding principle in Sec. I and used to validate the output in Sec. III F.
  • ad hoc to paper The branch pairing at the light cone is resolved by the specific complex path Eq. (10) with Im(theta) -> 0^-.
    Introduced in Sec. III E to assign complex branches; different choices of this path could alter which surfaces connect to which at theta = pi/2.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Temporal Entanglement from Holographic Entanglement Entropy." pith.science (2026). https://pith.science/paper/4WGPKU5T

@misc{pith2026250717847,
  author       = {Pith},
  title        = {Pith review of: Temporal Entanglement from Holographic Entanglement Entropy},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/4WGPKU5T}},
  note         = {Machine review of arXiv:2507.17847}
}
read the original abstract

Recently, several notions of entanglement in time have emerged as a novel frontier in quantum many-body physics, quantum field theory and gravity. We propose a systematic prescription to characterize temporal entanglement in relativistic quantum field theory in a general state for an arbitrary subregion on a flat, constant-time slice in a flat spacetime. Our prescriptions starts with the standard entanglement entropy of a spatial subregion and amounts to transporting the unchanged subregion to boosted time slices all the way across the light cone when it becomes in general a complex characterization of the corresponding temporal subregion. For holographic quantum field theories, our prescription amounts to an analytic continuation of all codimension-two bulk extremal surfaces satisfying the homology constraint and picking the one with the smallest real value of the area as the leading saddle point. We implement this prescription for holographic conformal field theories in thermal states on both a two-dimensional Lorentzian cylinder and three-dimensional Minkowski space, and show that it leads to results with self-consistent physical properties of temporal entanglement.

Figures

Figures reproduced from arXiv: 2507.17847 by the authors.

Figure 1
Figure 1. FIG. 1 [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. Geometry of a strip boundary subregion [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 4
Figure 4. FIG. 4. For a strip with [PITH_FULL_IMAGE:figures/full_fig_p005_4.png] view at source ↗
Figures from the paper (12 more)
Figure 3
Figure 3. Figure 3: FIG. 3 [PITH_FULL_IMAGE:figures/full_fig_p005_3.png]
Figure 5
Figure 5. Figure 5: FIG. 5 [PITH_FULL_IMAGE:figures/full_fig_p006_5.png]
Figure 7
Figure 7. Figure 7: FIG. 7. Relevant branches of complex extremal surfaces for [PITH_FULL_IMAGE:figures/full_fig_p007_7.png]
Figure 6
Figure 6. Figure 6: FIG. 6 [PITH_FULL_IMAGE:figures/full_fig_p007_6.png]
Figure 8
Figure 8. Figure 8: demonstrates that these complex surfaces, when θ is taken from π 4 + 10−4 to π 2 , always end up in the upper vacuum-connected branch of solutions shown in [PITH_FULL_IMAGE:figures/full_fig_p008_8.png]
Figure 9
Figure 9. Figure 9: FIG. 9. For [PITH_FULL_IMAGE:figures/full_fig_p009_9.png]
Figure 10
Figure 10. Figure 10: FIG. 10. For [PITH_FULL_IMAGE:figures/full_fig_p009_10.png]
Figure 12
Figure 12. Figure 12: FIG. 12. For a timelike strip with [PITH_FULL_IMAGE:figures/full_fig_p010_12.png]
Figure 13
Figure 13. Figure 13: (a). A geodesic with generic winding number n has length given by (14) with ∆ϕ → 2πn − ∆ϕ. Compare with γ1 in [PITH_FULL_IMAGE:figures/full_fig_p011_13.png]
Figure 14
Figure 14. Figure 14: FIG. 14. Emergence of null singularities along the rotation [PITH_FULL_IMAGE:figures/full_fig_p012_14.png]
Figure 15
Figure 15. Figure 15: FIG. 15. Analytic continuation of holographic entanglement [PITH_FULL_IMAGE:figures/full_fig_p013_15.png]
Figure 16
Figure 16. Figure 16: FIG. 16. Analytic continuation of holographic entanglement [PITH_FULL_IMAGE:figures/full_fig_p014_16.png]

Discussion (0). Sign in to comment.

Forward citations

Cited by 10 Pith papers

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

  1. Selecting Complex Extremal Surfaces with the Kontsevich--Segal--Witten Criterion

    hep-th 2026-07 conditional novelty 7.0 of 10

    In AdS3, dS3, and AdS4 hyperbolic examples, the Kontsevich-Segal-Witten criterion uniquely selects a three-piece complex contour for timelike extremal surfaces, while timelike strips in AdS4 violate the criterion near...

  2. Temporal Entanglement from Twist Correlators in 2d Conformal Field Theory and Holography

    hep-th 2026-07 conditional novelty 7.0 of 10

    Timelike entanglement entropy in 2d CFT is defined by time-ordered twist correlators, whose holographic saddles are complex geodesics with smallest real length, and whose imaginary part counts causal-diamond crossings...

  3. Linear Growth of Holographic Time-like Entanglement Entropy and Kasner exponents

    hep-th 2026-06 unverdicted novelty 6.5 of 10

    Late-time TEE growth in asymptotically AdS black holes with space-like singularities is governed by a critical extremal surface inside the horizon, with real/imaginary growth rates bounded by Schwarzschild-AdS under e...

  4. Analytic HTEE in Moving Plasmas and Its Transition

    hep-th 2026-07 conditional novelty 6.0 of 10

    Analytic holographic timelike entanglement entropy for a boosted BTZ black hole, with a critical boost separating complex and real extremal-geodesic branches.

  5. Timelike Entanglement First Law and Linearized Field Equations in Higher Curvature Gravity

    hep-th 2026-07 unverdicted novelty 6.0 of 10

    Timelike entanglement first law holds in Lovelock gravity about AdS, with both entropy and modular Hamiltonian variations carrying the same coupling factor that renormalizes Newton's constant in the linearized equations.

  6. Holographic Timelike Entanglement and Subregion Complexity in Localized AdS3*S3*T4 Black Holes

    hep-th 2026-07 conditional novelty 6.0 of 10

    Timelike entanglement and subregion complexity detect the cap–horizon transition of localized AdS3×S3×T4 black poles via fixed-boundary-interval Lorentzian branch selection, effects absent in BTZ and large-r limits.

  7. Composite AdS geodesics for CFT correlators and timelike entanglement entropy

    hep-th 2025-11 conditional novelty 6.0 of 10

    A bulk extremization prescription produces composite timelike-spacelike geodesics whose complex length exactly matches CFT two-point functions at timelike separation, including behind the BTZ horizon.

  8. Entanglement first law for timelike entanglement entropy and linearized Einstein's equation

    hep-th 2025-11 conditional novelty 6.0 of 10

    For timelike boundary regions, the entanglement first law ΔS = Δ⟨H⟩ is equivalent, by the paper's proof, to the linearized Einstein equations around AdS.

  9. Timelike Holographic Complexity

    hep-th 2025-10 conditional novelty 6.0 of 10

    Timelike subregion complexity within the holographic Complexity=Volume conjecture is computed for pure AdS and AdS black branes; it is purely real and shares the spacelike UV divergence structure.

  10. Entanglement measures for causally connected subregions and holography

    hep-th 2025-08 conditional novelty 6.0 of 10

    Timelike separated subregions admit a transition-operator entropy, a complexified RT surface, and a timelike entanglement wedge cross section that equals half the analytically continued reflected entropy in AdS3/CFT2.

Reference graph

Works this paper leans on

50 extracted references · 10 canonical work pages · cited by 10 Pith papers

  1. [28]

    M. P. Heller, F. Ori and A. Serantes, Geometric Interpretation of Timelike Entanglement Entropy , Phys. Rev. Lett. 134 (2025), no. 13 131601 [arXiv:2408.15752]

    arXiv 2025

  2. [1]

    Orus, A Practical Introduction to Tensor Networks: Matrix Product States and Projected Entangled Pair States, Annals Phys

    R. Orus, A Practical Introduction to Tensor Networks: Matrix Product States and Projected Entangled Pair States, Annals Phys. 349 (2014) 117–158 [arXiv:1306.2164]

    arXiv 2014

  3. [2]

    J. I. Cirac, D. Perez-Garcia, N. Schuch and F. Verstraete, Matrix product states and projected entangled pair states: Concepts, symmetries, theorems, Rev. Mod. Phys. 93 (2021), no. 4 045003 [arXiv:2011.12127]

    arXiv 2021

  4. [3]

    B. Zeng, X. Chen, D.-L. Zhou and X.-G. Wen, Quantum Information Meets Quantum Matter: From Quantum Entanglement to Topological Phases of Many-Body Systems. Quantum Science and Technology. Springer, 2019

    work page 2019

  5. [4]

    T. Mori, T. N. Ikeda, E. Kaminishi and M. Ueda, Thermalization and prethermalization in isolated quantum systems: a theoretical overview , J. Phys. B 51 (2018), no. 11 112001 [arXiv:1712.08790]

    arXiv 2018

  6. [5]

    Berges, M

    J. Berges, M. P. Heller, A. Mazeliauskas and R. Venugopalan, QCD thermalization: Ab initio approaches and interdisciplinary connections, Rev. Mod. Phys. 93 (2021), no. 3 035003 [arXiv:2005.12299]

    arXiv 2021

  7. [6]

    Casini and M

    H. Casini and M. Huerta, Lectures on entanglement in quantum field theory , PoS T ASI2021(2023) 002 [arXiv:2201.13310]

    arXiv 2023

  8. [7]

    Nishioka, S

    T. Nishioka, S. Ryu and T. Takayanagi, Holographic Entanglement Entropy: An Overview , J. Phys. A 42 (2009) 504008 [arXiv:0905.0932]

    arXiv 2009

Show all 50 references
  1. [8]

    Rangamani and T

    M. Rangamani and T. Takayanagi, Holographic Entanglement Entropy, vol. 931. Springer, 2017

    2017

  2. [9]

    B. Chen, B. Czech and Z.-z. Wang, Quantum information in holographic duality , Rept. Prog. Phys. 85 (2022), no. 4 046001 [arXiv:2108.09188]

    2022 arXiv

  3. [10]

    Almheiri, T

    A. Almheiri, T. Hartman, J. Maldacena, E. Shaghoulian and A. Tajdini, The entropy of Hawking radiation , Rev. Mod. Phys. 93 (2021), no. 3 035002 [arXiv:2006.06872]

    2021 arXiv

  4. [11]

    M. C. Ba˜ nuls, M. B. Hastings, F. Verstraete and J. I. Cirac, Matrix Product States for Dynamical Simulation of Infinite Chains , Phys. Rev. Lett. 102 (2009), no. 24 240603

    2009

  5. [12]

    M. B. Hastings and R. Mahajan, Connecting Entanglement in Time and Space: Improving the Folding Algorithm, Phys. Rev. A 91 (2015), no. 3 032306 [arXiv:1411.7950]

    2015 arXiv

  6. [13]

    Fr ´ ıas-P´ erez and M

    M. Fr ´ ıas-P´ erez and M. C. Ba˜ nuls,Light cone tensor network and time evolution , Phys. Rev. B 106 (2022), no. 11 115117 [arXiv:2201.08402]

    2022 arXiv

  7. [14]

    Lerose, M

    A. Lerose, M. Sonner and D. A. Abanin, Overcoming the entanglement barrier in quantum many-body dynamics 17 via space-time duality , Phys. Rev. B 107 (2023), no. 6 L060305 [arXiv:2201.04150]

    2023 arXiv

  8. [15]

    Giudice, G

    G. Giudice, G. Giudici, M. Sonner, J. Thoenniss, A. Lerose, D. A. Abanin and L. Piroli, Temporal Entanglement, Quasiparticles, and the Role of Interactions, Phys. Rev. Lett. 128 (2022), no. 22 220401 [arXiv:2112.14264]

    2022 arXiv

  9. [16]

    Carignano, C

    S. Carignano, C. R. Marim´ on and L. Tagliacozzo, Temporal entropy and the complexity of computing the expectation value of local operators after a quench , Phys. Rev. Res. 6 (2024), no. 3 033021 [arXiv:2307.11649]

    2024 arXiv

  10. [17]

    K. Doi, J. Harper, A. Mollabashi, T. Takayanagi and Y. Taki, Pseudoentropy in dS/CFT and Timelike Entanglement Entropy, Phys. Rev. Lett. 130 (2023), no. 3 031601 [arXiv:2210.09457]

    2023 arXiv

  11. [18]

    K. Doi, J. Harper, A. Mollabashi, T. Takayanagi and Y. Taki, Timelike entanglement entropy , JHEP 05 (2023) 052 [arXiv:2302.11695]

    2023 arXiv

  12. [19]

    Narayan, de Sitter space, extremal surfaces, and time entanglement, Phys

    K. Narayan, de Sitter space, extremal surfaces, and time entanglement, Phys. Rev. D 107 (2023), no. 12 126004 [arXiv:2210.12963]

    2023 arXiv

  13. [20]

    Holzhey, F

    C. Holzhey, F. Larsen and F. Wilczek, Geometric and renormalized entropy in conformal field theory , Nucl. Phys. B 424 (1994) 443–467 [arXiv:hep-th/9403108]

    1994 arXiv

  14. [21]

    Calabrese and J

    P. Calabrese and J. L. Cardy, Entanglement entropy and quantum field theory , J. Stat. Mech. 0406 (2004) P06002 [arXiv:hep-th/0405152]

    2004 arXiv

  15. [22]

    Carignano and L

    S. Carignano and L. Tagliacozzo, Loschmidt echo, emerging dual unitarity and scaling of generalized temporal entropies after quenches to the critical point , arXiv:2405.14706

  16. [23]

    Ryu and T

    S. Ryu and T. Takayanagi, Holographic derivation of entanglement entropy from AdS/CFT , Phys. Rev. Lett. 96 (2006) 181602 [arXiv:hep-th/0603001]

    2006 arXiv

  17. [24]

    V. E. Hubeny, M. Rangamani and T. Takayanagi, A Covariant holographic entanglement entropy proposal , JHEP 07 (2007) 062 [arXiv:0705.0016]

    2007 arXiv

  18. [25]

    Casini, M

    H. Casini, M. Huerta and R. C. Myers, Towards a derivation of holographic entanglement entropy , JHEP 05 (2011) 036 [arXiv:1102.0440]

    2011 arXiv

  19. [26]

    Lewkowycz and J

    A. Lewkowycz and J. Maldacena, Generalized gravitational entropy, JHEP 08 (2013) 090 [arXiv:1304.4926]

    2013 arXiv

  20. [27]

    X. Dong, A. Lewkowycz and M. Rangamani, Deriving covariant holographic entanglement, JHEP 11 (2016) 028 [arXiv:1607.07506]

    2016 arXiv

  21. [29]

    Fidkowski, V

    L. Fidkowski, V. Hubeny, M. Kleban and S. Shenker, The Black hole singularity in AdS / CFT , JHEP 02 (2004) 014 [arXiv:hep-th/0306170]

    2004 arXiv

  22. [30]

    Balasubramanian, A

    V. Balasubramanian, A. Bernamonti, B. Craps, V. Ker¨ anen, E. Keski-Vakkuri, B. M¨ uller, L. Thorlacius and J. Vanhoof, Thermalization of the spectral function in strongly coupled two dimensional conformal field theories, JHEP 04 (2013) 069 [arXiv:1212.6066]

    2013 arXiv

  23. [31]

    ˇCeplak, H

    N. ˇCeplak, H. Liu, A. Parnachev and S. Valach, Black hole singularity from OPE , JHEP 10 (2024) 105 [arXiv:2404.17286]

    2024 arXiv

  24. [32]

    Headrick, Entanglement Renyi entropies in holographic theories, Phys

    M. Headrick, Entanglement Renyi entropies in holographic theories, Phys. Rev. D 82 (2010) 126010 [arXiv:1006.0047]

    2010 arXiv

  25. [33]

    F. M. Haehl, T. Hartman, D. Marolf, H. Maxfield and M. Rangamani, Topological aspects of generalized gravitational entropy, JHEP 05 (2015) 023 [arXiv:1412.7561]

    2015 arXiv

  26. [34]

    Susskind and E

    L. Susskind and E. Witten, The Holographic bound in anti-de Sitter space , arXiv:hep-th/9805114

    arXiv

  27. [35]

    Nunez and D

    C. Nunez and D. Roychowdhury, Interpolating between Space-like and Time-like Entanglement via Holography , arXiv:2507.17805

  28. [36]

    Kusuki, T

    Y. Kusuki, T. Takayanagi and K. Umemoto, Holographic Entanglement Entropy on Generic Time Slices , JHEP 06 (2017) 021 [arXiv:1703.00915]

    2017 arXiv

  29. [37]

    B. Liu, H. Chen and B. Lian, Entanglement entropy of free fermions in timelike slices , Phys. Rev. B 110 (2024), no. 14 144306 [arXiv:2210.03134]

    2024 arXiv

  30. [38]

    Erdmenger and N

    J. Erdmenger and N. Miekley, Non-local observables at finite temperature in AdS/CFT , JHEP 03 (2018) 034 [arXiv:1709.07016]

    2018 arXiv

  31. [39]

    Banados, C

    M. Banados, C. Teitelboim and J. Zanelli, The Black hole in three-dimensional space-time , Phys. Rev. Lett. 69 (1992) 1849–1851 [arXiv:hep-th/9204099]

    1992 arXiv

  32. [40]

    Balasubramanian, B

    V. Balasubramanian, B. D. Chowdhury, B. Czech and J. de Boer, Entwinement and the emergence of spacetime , JHEP 01 (2015) 048 [arXiv:1406.5859]

    2015 arXiv

  33. [41]

    V. E. Hubeny, M. Rangamani and E. Tonni, Global properties of causal wedges in asymptotically AdS spacetimes, JHEP 10 (2013) 059 [arXiv:1306.4324]

    2013 arXiv

  34. [42]

    V. E. Hubeny, H. Liu and M. Rangamani, Bulk-cone singularities & signatures of horizon formation in AdS/CFT, JHEP 01 (2007) 009 [arXiv:hep-th/0610041]

    2007 arXiv

  35. [43]

    M. Gary, S. B. Giddings and J. Penedones, Local bulk S-matrix elements and CFT singularities , Phys. Rev. D 80 (2009) 085005 [arXiv:0903.4437]

    2009 arXiv

  36. [44]

    Maldacena, D

    J. Maldacena, D. Simmons-Duffin and A. Zhiboedov, Looking for a bulk point , JHEP 01 (2017) 013 [arXiv:1509.03612]

    2017 arXiv

  37. [45]

    Dodelson, C

    M. Dodelson, C. Iossa, R. Karlsson, A. Lupsasca and A. Zhiboedov, Black hole bulk-cone singularities , JHEP 07 (2024) 046 [arXiv:2310.15236]

    2024 arXiv

  38. [46]

    Czech, L

    B. Czech, L. Lamprou, S. McCandlish and J. Sully, Integral Geometry and Holography, JHEP 10 (2015) 175 [arXiv:1505.05515]

    2015 arXiv

  39. [47]

    de Boer, M

    J. de Boer, M. P. Heller, R. C. Myers and Y. Neiman, Holographic de Sitter Geometry from Entanglement in Conformal Field Theory , Phys. Rev. Lett. 116 (2016), no. 6 061602 [arXiv:1509.00113]

    2016 arXiv

  40. [48]

    Czech, L

    B. Czech, L. Lamprou, S. McCandlish, B. Mosk and J. Sully, A Stereoscopic Look into the Bulk , JHEP 07 (2016) 129 [arXiv:1604.03110]

    2016 arXiv

  41. [49]

    de Boer, F

    J. de Boer, F. M. Haehl, M. P. Heller and R. C. Myers, Entanglement, holography and causal diamonds , JHEP 08 (2016) 162 [arXiv:1606.03307]

    2016 arXiv

  42. [50]

    Milekhin, Z

    A. Milekhin, Z. Adamska and J. Preskill, Observable and computable entanglement in time , arXiv:2502.12240

Pith tools

Reviewed August 6, 2026 · model on record in the stance chip above.