Pith. sign in

REVIEW 4 major objections 6 minor 98 references

The thread embodiment of holographic quantum entanglement

T0 review · 4 major / 6 minor · reviewed 2026-08-10 · deepseek-v4-flash

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

Pith's one-line read Holographic entanglement can be encoded by a unique collection of bulk threads whose trajectories are exactly geodesics, turning kinematic space into a circuit board.

desk verdict A coherent and honest framework proposal for holographic entanglement threads, but the central geodesic claim is a labeled conjecture and its verification runs in circles; worth refereeing, not worth treating as derived. read the letter →

arxiv 2501.10691 v4 pith:EHMRRX5G submitted 2025-01-18 hep-th quant-ph

Yi-Yu Lin This is my paper · ORCID
classification hep-thquant-ph
keywords holographicentanglemententropythreadsbitkinematicspacecomplexityRyu-Takayanagiformulatensornetworksthread-statecorrespondence
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

The paper sets out to show that the entanglement structure of a holographic spacetime can be encoded, without loss, in a collection of bulk curves called entanglement threads: one thread per unit of Ryu-Takayanagi surface area, with the number of threads between two boundary subregions equal to half the conditional mutual information of those subregions. Its central new claim is that the trajectory of every thread in a spatial slice is exactly a geodesic, reached by applying a 'no-return' rule—a thread may cross a given simply connected RT surface only once—and then shrinking the boundary regions to a limit. If this claim is right, the thread configuration is not an arbitrary bookkeeping device but a unique canonical structure: kinematic space becomes a circuit board whose wires are the threads and whose gate count reproduces holographic complexity, while the whole configuration encodes entanglement between bulk surfaces through the generalized RT formula. A sympathetic reader would care because the paper turns a visual metaphor into a precise, checkable proposal about how quantum information is organized in the bulk.

What carries the argument

The load-bearing objects are the entanglement threads themselves: boundary-anchored bulk curves with fluxes fixed by $F_{ij} = \frac{1}{2}I(A_i, A_j | L)$. The argument's engine is the no-return rule—an entanglement thread may not cross a given simply connected RT surface more than once, because each unit area of that surface accommodates exactly one thread connecting the two complementary boundary regions; squeezing two boundary regions small confines the intervening thread to a narrowing channel between RT surfaces, so in the limit its trajectory must be a geodesic. Kinematic space, the space of all boundary-anchored geodesics equipped with the Crofton form, then acts as the organizing board: each geodesic is a wire, each geodesic intersection a quantum gate, and the integral formula $\mathrm{vol}(X)/4G_N = \frac{1}{2\pi}\int_{G_X}\lambda_X\,\omega$ converts bulk volume into gate count, giving complexity a circuit meaning. Thread-state correspondence assigns each thread the state $|\zeta\rangle$, so the entire configuration is a tensor product state whose reduced density matrices yield generalized RT entropies.

What would settle it

Compute the unique thread fluxes $F_{ij}$ from Eq. (5) for a fine boundary partition in a non-simply-connected or time-dependent bulk, such as a BTZ geometry or a multi-boundary wormhole, and check whether the minimal thread configuration consistent with all entropies necessarily contains a thread crossing some simply connected RT surface twice; if such a configuration exists, the no-return rule fails and the geodesic-trajectory conclusion falls, while if every satisfying configuration obeys the rule, the central claim is supported.

Watch

Extended reading notes

Core claim

The discovery, on the paper's own terms, is a complete geometric embodiment of holographic entanglement: define an entanglement thread as a one-dimensional curve in a codimension-one bulk slice with endpoints on the boundary, populated so that each unit area of an RT surface carries one thread. The paper argues that for any partition of the boundary into elementary regions, the number of threads connecting regions $A_i$ and $A_j$ is fixed by $F_{ij} = \frac{1}{2}I(A_i, A_j | L)$, half the conditional mutual information, and that the 'no-return' rule—a thread cannot pass through a given simply connected RT surface more than once—forces each thread's actual trajectory to be a geodesic. From there it shows that kinematic space organizes the threads: each geodesic is a wire, intersecting geodesics are coupled by a quantum gate, and the CV complexity of a bulk region equals the total number of gates in this canonical circuit. Interpreting each thread as the state $|\zeta\rangle = \frac{1}{\sqrt{2}}(|0_1\cdots 0_n\rangle + |1_1\cdots 1_n\rangle)$ makes the full thread configuration a tensor product state whose partial traces reproduce the generalized RT formula for arbitrary bulk surfaces, and distinguishes entanglement threads from bit threads because the entanglement-thread configuration is unique.

Load-bearing premise

The argument rests on the no-return rule: an entanglement thread cannot cross a given simply connected Ryu-Takayanagi surface more than once, a rule inferred from matching thread count to surface area rather than derived; if a thread could legally cross an RT surface twice, the limiting trajectory need not be a geodesic and the uniqueness of the thread configuration would collapse.

Editorial extensions

If this is right

  • Every boundary entanglement entropy and every generalized RT entropy is reproduced by one unique thread configuration, so the thread picture is a complete refinement of the RT formula rather than one of many equivalent decompositions.
  • Kinematic space functions as a canonical circuit board: geodesic wires, gates at intersections, and CV complexity equal to the gate count make holographic complexity a derived circuit quantity.
  • The thread configuration provides a partial-order scaffold on which the true holographic state is built by inserting quantum gates, so the entanglement structure is fixed before the details of gates or metric are specified.
  • Entanglement threads and bit threads differ in uniqueness: bit threads are non-unique optimal flows with a density bound, while entanglement threads are unique geodesics; different bit-thread configurations correspond to different apparent-wire conventions in the same quantum circuit.

Reading between the lines

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

  • If the geodesic-trajectory claim is right, the no-return rule effectively selects a preferred foliation of holographic entanglement: the unique thread configuration gives a canonical reference point for comparing different tensor-network and surface-state constructions.
  • A concrete testable extension is to apply the same no-return construction to BTZ or multi-boundary wormhole geometries, where the paper notes the flux computation requires kinematic-space integral geometry rather than sums of RT areas; a direct calculation there would probe whether geodesic trajectories survive.
  • Treating a thread's trajectory as a partial order rather than a metric geodesic suggests the thread picture may persist in metric-free or discrete settings, offering a way to discuss entanglement structure before geometry emerges—an idea the paper gestures at without developing quantitatively.
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 / 6 minor

Summary. The paper develops a 'thread' picture of holographic entanglement. It argues that the number of entanglement threads connecting boundary regions is given by half the conditional mutual information (Eq. 5); that each thread's trajectory in the bulk is precisely a geodesic (Section 3.1); and that kinematic space provides a canonical quantum circuit representation in which each thread is a wire, each geodesic intersection is a gate, and holographic complexity becomes a gate count (Section 4.2). The paper also proposes a thread-state correspondence (Section 5.1) and compares the construction with bit threads (Section 5.2). The presentation is clear and connects many existing ideas, but the central derivation relies on the unproven 'no-return' rule and the kinematic-space verification is circular.

Significance. If the central claims held, the paper would provide a concrete, unique, geodesic encoding of holographic entanglement that reproduces entanglement entropies, the generalized RT formula, and the CV complexity as a gate count. The paper is ambitious and clearly written, and it offers a unified perspective on bit threads, kinematic space, surface-state correspondence, and HaPPY tensor networks, with a falsifiable circuit interpretation of complexity. It also makes explicit predictions, such as the thread-state product form (14) and the generalized RT formula via thread flux, which could in principle be tested against tensor-network models. However, the geodesic-trajectory claim is not established: it rests on the no-return rule, which is introduced as a 'phenomenological fact' and acknowledged by the authors as a conjecture (Sections 3.1, 3.2, 4.2, 5.2), and Section 4.1's verification assumes geodesics from the outset. As it stands, the paper is best viewed as a proposal with consistency checks rather than a derivation from established holographic entanglement data.

major comments (4)
  1. [Section 3.1, Figure 4] The claim that thread trajectories are precisely geodesics depends entirely on the 'no-return' rule, which is stated as a phenomenological fact but not derived from the area-matching prescription of Section 2.1. The limiting argument in Figure 4b requires that a thread connecting A_i and A_j cross each of γ_L and γ_R exactly once; without the no-return rule, a thread could cross one of these surfaces multiple times, and the 'narrow channel' confinement would not follow. The paper itself flags the status of this step ('it is not hard to conjecture' in Section 3.1, 'we boldly conjectured' in Section 3.2, 'a non-trivial assertion' in Section 4.2, 'we have asserted' in Section 5.2). Since the geodesic claim underlies the uniqueness of the thread configuration, the kinematic-space circuit, and the complexity interpretation, this is load-bearing. Please either derive the no-return rule from more basic assumptions or explicitly present the geodesic trajectory as a conjecture throughout, and adjust the language of 'demonstration' and 'verification' accordingly.
  2. [Section 4.1, Eqs. (9) and (11)] Section 4.1 claims to 'verify that the trajectories of entanglement threads are indeed geodesics' by computing F^{σ1σ4}_{13} with kinematic-space integrals and finding consistency with Eq. (9). However, Eq. (9) was derived in Section 3.2 using the no-return rule and the thread fluxes from Section 2.1, and the computation in Section 4.1 assumes from the start that threads are geodesics. The agreement is therefore a consistency check of the geodesic ansatz with the already-assumed flux formulas, not an independent verification. Please rephrase this section as a consistency check under the geodesic assumption, and state explicitly what evidence would count against the geodesic assumption.
  3. [Section 5.1, Eqs. (13), (14), (22)] The thread-state correspondence is introduced by stipulation: each thread is assigned the state |ζ> = (|0...0>+|1...1>)/√2 and the full configuration is the product state (14). The subsequent derivation of the density matrix (22) and the 'generalized RT formula' uses the fact that only threads with one endpoint on a surface contribute to its entanglement entropy; this is essentially the same area-matching condition used to define the threads in Section 2.1. The closing claim that the generalized RT formula is 'satisfied everywhere' is therefore a consistency property of the construction, not a prediction derived from independent data. Please state explicitly which elements are definitions, which are consistency checks, and which are falsifiable predictions.
  4. [Section 5.2] The uniqueness assertion ('our entanglement thread configuration is unique—since we have asserted that each thread's trajectory is precisely a bulk geodesic') is presented without proof. Even accepting the geodesic ansatz, the construction involves choices: the regularization of kinematic space into 'unit-volume diamonds' (Section 4.2), the mapping from continuous geodesics to discrete threads, and the gluing of boundary-anchored geodesics into a complete set of threads all require conventions. Please state the precise sense in which the configuration is unique and identify which elements are fixed by the entropy data and which are conventional.
minor comments (6)
  1. [Abstract and title page] The phrase 'a elegant circuit interpretation' should be 'an elegant circuit interpretation'.
  2. [Section 3.1] There is a missing space in 'the entanglement threadζij' and 'a serious of adjacent arrows' should be 'a series of adjacent arrows'.
  3. [Section 5.1] The word 'didentity' appears in the sentence about trivial identity evolution; this appears to be a typo for 'identity'.
  4. [Section 5.2] There is a missing space in 'the concept ofbit threads'; it should be 'the concept of bit threads'.
  5. [Eq. (13) and surrounding text] The paper uses 'qudit' dimensions d in some places and writes the thread state as a two-level |0>/|1> superposition; please clarify whether each thread carries a qubit or a qudit, and whether Eq. (13) holds for general d or only for d=2.
  6. [Section 4.2] The regularization 'divide kinematic space into small diamonds with volume equal to 1' is invoked but not specified; please state how the volume normalization is fixed relative to the Crofton form (34), and whether the results depend on the chosen cell size.

Circularity Check

2 steps flagged · score 6.0 of 10

The geodesic-trajectory claim is verified only under its own assumption, and the generalized RT result is built into the thread-state definition; the derivation chain is partially circular.

  1. other [Section 3.1 (no-return rule and geodesic conjecture) and Section 4.1 (Eqs. 9-11)]
    "According to this "no-return" rule of entanglement threads on RT surfaces, it is not hard to conjecture that the trajectories of entanglement threads in the bulk should coincide with geodesics. ... Since we now assume that the trajectories of these entanglement threads precisely coincide with geodesics, it becomes relatively straightforward ... Thus, (11) is completely consistent with (9)."

    The geodesic conclusion is inferred from the no-return rule, which is itself an extra stipulation introduced to make the area-matching prescription work, not derived from entanglement data. The Section 4.1 'verification' then takes the geodesic hypothesis as an input: it computes a flux in kinematic space by assuming threads are geodesics and checks that the result equals Eq. (9), a combination already fixed by the area constraints and no-return routing in Section 3.2. Matching Eq. (11) to Eq. (9) is therefore a consistency check between two calculations sharing the same inputs, not an independent confirmation that threads are geodesics. The paper itself repeatedly calls the geodesic statement a conjecture, so the central claim remains assumed rather than derived.

  2. self definitional [Section 5.1, Eqs. (13)-(22) and the generalized RT paragraph]
    "while for a thread passing through σ3, its endpoint qubits (one on σ3, one on its complement) entangled in a Bell state, which leads to: ρσ3 = ... The exponent here denotes the number of threads with one end on surface σ3 and the other on its complement. Clearly, the von Neumann entropy of σ3 is exactly equal to this number. ... We thus obtain a formulation of the generalized Ryu-Takayanagi (RT) formula."

    The thread state |ζ> is defined in Eq. (13) as a Bell-like superposition over all qudits a thread traverses, and the full state |Ψ> in Eq. (14) is the tensor product of such states. Tracing out the complement then yields a reduced density matrix whose entropy is one unit per thread by construction (Eq. (22)). The thread fluxes appearing in the exponent were previously solved in Section 3.2 to reproduce area combinations (Eqs. (7)-(9)). Hence the 'generalized RT formula' obtained here — entropy of σ̃3 equals area(σ3)/4GN — is an identity assembled from the definitions: the reduced state was engineered to have Bell-pair entropy, and the thread count was set equal to the area. The agreement is a self-consistency check, not a prediction from independent ingredients.

full rationale

The paper is transparent about the conjectural status of its central geometric claim: the geodesic trajectory is introduced via an unproved 'no-return' rule and is later checked rather than derived. That check (Eq. (11) reproducing Eq. (9)) assumes the geodesic hypothesis in the kinematic-space calculation, so it cannot independently establish the hypothesis; the uniqueness of the thread configuration asserted in Section 5.2 therefore rests on that assumption. Likewise, the thread-state correspondence is defined so that each thread contributes one Bell pair to any surface it crosses, and the thread fluxes were fixed to area values earlier, so the generalized RT entropy formula follows by construction rather than as an independent result. The half-CMI flux formula (Eq. (5)) is imported from the author's own [24]; this is a load-bearing self-citation, but since the underlying linear-system solution is a mathematical identity and the paper does not otherwise redefine it, I do not count it as the main circular step. Overall, the derivations are largely consistency demonstrations of an ansatz; because the paper is explicit about their conditional character, the circularity is partial rather than total.

Assumptions & free parameters 0 free parameters · 8 assumptions · 3 invented entities

The framework rests on several postulates: the RT area prescription, the CMI thread-count formula imported from the author's [24], the no-return rule, the geodesic trajectory assumption, surface-state correspondence, and the thread-state correspondence. None of these has a falsifiable handle outside the framework, and several are introduced specifically to make the picture work.

assumptions (8)
  • domain assumption RT formula: S(A)=Area(γ_A)/(4G_N), with 4G_N=1.
    Assumed throughout as the input relation between boundary entropy and bulk area; Section 2.1.
  • domain assumption Thread count F_ij=1/2 I(A_i,A_j|L) is the unique solution for thread fluxes from interval entropies.
    Imported from the author's earlier paper [24]; the present paper does not re-derive it. Section 2.1, Eq. (5).
  • ad hoc to paper No-return rule: an entanglement thread crosses a given simply connected RT surface at most once.
    Postulated in Section 3.1 as a 'phenomenological fact' derived from area matching; it drives the geodesic conclusion.
  • ad hoc to paper Trajectories of entanglement threads are geodesics in the bulk.
    Conjectured from the no-return rule in Section 3.1 and used as an input in the kinematic-space checks of Section 4.1.
  • domain assumption Surface-state correspondence: a bulk subregion bounded by RT surfaces corresponds to a pure state whose boundary regions have entropies equal to their areas.
    Taken from prior surface-state correspondence literature [40,41] and used in Section 3.2 to generate constraints (7) and (8).
  • ad hoc to paper Thread-state correspondence: each thread carries |ζ>=(|0...0>+|1...1>)/√2, and the whole configuration is the product state |Ψ> = ⊗_ζ |ζ>.
    Proposed in Section 5.1; it is constructed so that trace over a surface yields Bell-like reduced states and the generalized RT formula.
  • ad hoc to paper Kinematic space can be regularized into unit-volume diamonds, each representing one thread, and each geodesic intersection becomes a quantum gate.
    Footnote 9 and Section 4.2; this discretization makes the CV volume integral count gates by construction.
  • ad hoc to paper The holographic state is obtained by adding gates on top of the thread state |Ψ>, and complexity is the number of gates.
    Proposed in Sections 4.2 and 5.1; no explicit circuit optimization or reference state is specified.
invented entities (3)
  • Entanglement thread as a unique geodesic wire with unit flux
    purpose: Represents one unit of entanglement between boundary regions and acts as a circuit wire in the canonical quantum circuit.
    The paper defines its trajectory via the no-return rule and geodesic assumption; there is no measurement or falsifiable prediction attached.
  • Thread-state |ζ> = (|0...0>+|1...1>)/√2
    purpose: Assigns a global multipartite entangled state to each thread so that any surface cut reproduces Bell-like reduced density matrices.
    Introduced in Section 5.1; its consequences follow by construction rather than from independent data.
  • Kinematic space as a circuit input board
    purpose: Organizes qudits and gates: each point (u,v) is an input wire, and the diamond region ♢_uv determines which gates couple that wire.
    Proposed in Section 4.2 as an interpretation; the wire/gate assignment is fixed by the unit-volume discretization.

how reviews work

0 comments
Cite this review

Pith. "Pith review of The thread embodiment of holographic quantum entanglement." pith.science (2026). https://pith.science/paper/EHMRRX5G

@misc{pith2026250110691,
  author       = {Pith},
  title        = {Pith review of: The thread embodiment of holographic quantum entanglement},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/EHMRRX5G}},
  note         = {Machine review of arXiv:2501.10691}
}
read the original abstract

This paper systematically develops the concept of entanglement threads that characterize the entanglement structure of holographic duality. Behind this framework lies a simple philosophy: holographic quantum entanglement can be visualized using thread-like objects. Inspired by the fact that tensor network models can be deformed into a quantum circuit form with flow-conserving features, we abstract the concept of entanglement threads. These entanglement threads can be understood as a pre-set ensemble of wires in a holographic quantum circuit, and we propose that they characterize the underlying partially ordered structure of holographic quantum entanglement. Combining the concepts of entanglement threads and kinematic space, a elegant circuit interpretation for the holographic complexity is provided. We also clarify the connection and distinction between entanglement threads and the previously proposed concept of bit threads.

Figures

Figures reproduced from arXiv: 2501.10691 by the authors.

Figure 1
Figure 1. (a) A holographic “thread” picture characterizing the entanglement entropy be [PITH_FULL_IMAGE:figures/full_fig_p006_1.png] view at source ↗
Figure 2
Figure 2. A simplified network diagram corresponding to the entanglement thread configu [PITH_FULL_IMAGE:figures/full_fig_p008_2.png] view at source ↗
Figure 3
Figure 3. (a) HaPPY tensor network state and an RT surface (red dashed line) which [PITH_FULL_IMAGE:figures/full_fig_p010_3.png] view at source ↗
Figures from the paper (11 more)
Figure 4
Figure 4. Figure 4: (a) Some counterexamples that violate the thread trajectory rules. (b) By contin [PITH_FULL_IMAGE:figures/full_fig_p013_4.png]
Figure 5
Figure 5. Figure 5: A decomposition of the bulk slice W into four parts W1, W2, W3, W4 by two intersecting RT surfaces γ12 = σ3 ∪σ4 and γ23 = σ1 ∪σ2. Further considering the trajectory of the entanglement threads in each fragment, now a total of 8 independent thread bundles (each bundle i…
Figure 6
Figure 6. Figure 6: (a) Some geodesics accounting for F σ1σ4 13 are shown. (b) The set of geodesics contributing to F σ1σ4 13 corresponds to the orange region, which is the intersection of the red and yellow regions. 4 Entanglement Threads, Kinematic Space, and Quantum Circuits 4.1 Charac…
Figure 7
Figure 7. Figure 7: Regarding kinematic space as an input board, a qubit ( [PITH_FULL_IMAGE:figures/full_fig_p021_7.png]
Figure 8
Figure 8. Figure 8: The volume of a bulk region X (marked in grey) can be given by an integral over the length of all geodesic chords (marked in green). enclosed by its corresponding RT surface gives the complexity of the reduced density ma￾trix for A. Specifically, when A is taken to be …
Figure 9
Figure 9. Figure 9: (a) Focusing on a geodesic (marked in red) that passes through the [PITH_FULL_IMAGE:figures/full_fig_p024_9.png]
Figure 10
Figure 10. Figure 10: (a) The “thread-state correspondence”, first hypothesized in [ [PITH_FULL_IMAGE:figures/full_fig_p026_10.png]
Figure 11
Figure 11. Figure 11: Due to the conservation of the number of qubits, we have a certain degree [PITH_FULL_IMAGE:figures/full_fig_p030_11.png]
Figure 12
Figure 12. Figure 12: (a) α is the half-opening angle of the geodesic, and θ marks the center point of the corresponding boundary subregion. (b) Each point in kinematic space K represents a geodesic in the original space N. Appendix A Review of Kinematic Space A.1 Kinematic Space and the C…
Figure 13
Figure 13. Figure 13: (a) A point-curve in K corresponding to a point in N. (b) Computing the geodesic distance between two boundary points in N. Note that half of K space already contains all the geodesic information in N space. set of all such geodesics forms a trajectory in kinematic sp…
Figure 14
Figure 14. Figure 14: The half-qCMI has a direct and intuitive geometric interpretation in kinematic [PITH_FULL_IMAGE:figures/full_fig_p040_14.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

98 extracted references · 17 canonical work pages

  1. [1]

    The Large N limit of superconformal field theories and supergrav- ity,

    J. M. Maldacena, “The Large N limit of superconformal field theories and supergrav- ity,” Adv. Theor. Math. Phys. 2, 231-252 (1998) [arXiv:hep-th/9711200 [hep-th]]

    arXiv 1998

  2. [2]

    Gauge theory correlators from noncritical string theory,

    S. S. Gubser, I. R. Klebanov and A. M. Polyakov, “Gauge theory correlators from noncritical string theory,” Phys. Lett. B 428, 105-114 (1998) [arXiv:hep-th/9802109 [hep-th]]

    arXiv 1998

  3. [3]

    Anti-de Sitter space and holography,

    E. Witten, “Anti-de Sitter space and holography,” Adv. Theor. Math. Phys. 2, 253- 291 (1998) [arXiv:hep-th/9802150 [hep-th]]

    arXiv 1998

  4. [4]

    Holographic derivation of entanglement entropy from AdS/CFT,

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

    arXiv 2006

  5. [5]

    Aspects of Holographic Entanglement Entropy,

    S. Ryu and T. Takayanagi, “Aspects of Holographic Entanglement Entropy,” JHEP 08, 045 (2006) [arXiv:hep-th/0605073 [hep-th]]

    arXiv 2006

  6. [6]

    A Covariant holographic entan- glement entropy proposal,

    V. E. Hubeny, M. Rangamani and T. Takayanagi, “A Covariant holographic entan- glement entropy proposal,” JHEP 07, 062 (2007) [arXiv:0705.0016 [hep-th]]

    arXiv 2007

  7. [7]

    Entanglement Renormalization and Holography,

    B. Swingle, “Entanglement Renormalization and Holography,” Phys. Rev. D 86, 065007 (2012) [arXiv:0905.1317 [cond-mat.str-el]]

    arXiv 2012

  8. [8]

    Constructing holographic spacetimes using entanglement renormaliza- tion,

    B. Swingle, “Constructing holographic spacetimes using entanglement renormaliza- tion,” [arXiv:1209.3304 [hep-th]]. 41

    arXiv

Show all 98 references
  1. [9]

    Entanglement Renormalization,

    G. Vidal, “Entanglement Renormalization,” Phys. Rev. Lett. 99, no.22, 220405 (2007) [arXiv:cond-mat/0512165 [cond-mat]]

    2007 arXiv

  2. [10]

    Class of Quantum Many-Body States That Can Be Efficiently Simulated,

    G. Vidal, “Class of Quantum Many-Body States That Can Be Efficiently Simulated,” Phys. Rev. Lett. 101, 110501 (2008) [arXiv:quant-ph/0610099 [quant-ph]]

    2008 arXiv

  3. [11]

    Tensor network renormalization yields the multiscale entangle- ment renormalization ansatz,

    E. Glen, G. Vidal, “Tensor network renormalization yields the multiscale entangle- ment renormalization ansatz,” Phys. Rev. Lett. 115,200401 (2015)

    2015

  4. [12]

    Bit threads and holographic entanglement,

    M. Freedman and M. Headrick, “Bit threads and holographic entanglement,” Com- mun. Math. Phys. 352, no.1, 407-438 (2017) [arXiv:1604.00354 [hep-th]]

    2017 arXiv

  5. [13]

    Bit Threads and Holographic Monogamy,

    S. X. Cui, P. Hayden, T. He, M. Headrick, B. Stoica and M. Walter, “Bit Threads and Holographic Monogamy,” Commun. Math. Phys. 376, no.1, 609-648 (2019) [arXiv:1808.05234 [hep-th]]

    2019 arXiv

  6. [14]

    Riemannian and Lorentzian flow-cut theorems,

    M. Headrick and V. E. Hubeny, “Riemannian and Lorentzian flow-cut theorems,” Class. Quant. Grav. 35, no.10, 10 (2018) [arXiv:1710.09516 [hep-th]]

    2018 arXiv

  7. [15]

    Covariant bit threads,

    M. Headrick and V. E. Hubeny, “Covariant bit threads,” JHEP 07, 180 (2023) [arXiv:2208.10507 [hep-th]]

    2023 arXiv

  8. [16]

    Maximal Flow Through a Network,

    L. R. Ford, D. R. Fulkerson, “ Maximal Flow Through a Network,” Canad. J. Math. 8 (1956) 399–404

    1956

  9. [17]

    Note on maximal flow through a network,

    P. Elias, A. Feinstein, and C. Shannon, “ Note on maximal flow through a network,” IRE Transactions on Information Theory IT-2 (1956) 117–199

    1956

  10. [18]

    Concentrating partial entanglement by local operations,

    C. H. Bennett, H. J. Bernstein, S. Popescu and B. Schumacher, “Concentrating partial entanglement by local operations,” Phys. Rev. A 53, 2046-2052 (1996) [arXiv:quant- ph/9511030 [quant-ph]]

    1996

  11. [19]

    Purification of noisy entanglement and faithful teleportation via noisy chan- nels,

    C. H. Bennett, G. Brassard, S. Popescu, B. Schumacher, J. A. Smolin and W. K. Woot- ters, “Purification of noisy entanglement and faithful teleportation via noisy chan- nels,” Phys. Rev. Lett. 76, 722-725 (1996) [arXiv:quant-ph/9511027 [quant-ph]]

    1996 arXiv

  12. [20]

    Mixed state entanglement and quantum error correction,

    C. H. Bennett, D. P. DiVincenzo, J. A. Smolin and W. K. Wootters, “Mixed state entanglement and quantum error correction,” Phys. Rev. A 54, 3824-3851 (1996) [arXiv:quant-ph/9604024 [quant-ph]]. 42

    1996 arXiv

  13. [21]

    Integral Geometry and Hologra- phy,

    B. Czech, L. Lamprou, S. McCandlish and J. Sully, “Integral Geometry and Hologra- phy,” JHEP 10, 175 (2015) [arXiv:1505.05515 [hep-th]]

    2015 arXiv

  14. [22]

    Tensor Networks from Kinematic Space,

    B. Czech, L. Lamprou, S. McCandlish and J. Sully, “Tensor Networks from Kinematic Space,” JHEP 07, 100 (2016) [arXiv:1512.01548 [hep-th]]

    2016 arXiv

  15. [23]

    Distilled density matrices of holographic partial entanglement en- tropy from thread-state correspondence,

    Y. Y. Lin, “Distilled density matrices of holographic partial entanglement en- tropy from thread-state correspondence,” Phys. Rev. D 108, no.10, 106010 (2023) [arXiv:2305.02895 [hep-th]]

    2023 arXiv

  16. [24]

    Deriving the PEE proposal from the locking bit thread configuration,

    Y. Y. Lin, J. R. Sun and J. Zhang, “Deriving the PEE proposal from the locking bit thread configuration,” JHEP 10, 164 (2021) [arXiv:2105.09176 [hep-th]]

    2021 arXiv

  17. [25]

    The Holographic Entropy Cone,

    N. Bao, S. Nezami, H. Ooguri, B. Stoica, J. Sully and M. Walter, “The Holographic Entropy Cone,” JHEP 09, 130 (2015) [arXiv:1505.07839 [hep-th]]

    2015 arXiv

  18. [26]

    The holographic entropy arrangement,

    V. E. Hubeny, M. Rangamani and M. Rota, “The holographic entropy arrangement,” Fortsch. Phys. 67, no.4, 1900011 (2019) [arXiv:1812.08133 [hep-th]]

    2019 arXiv

  19. [27]

    Holographic entropy relations,

    V. E. Hubeny, M. Rangamani and M. Rota, “Holographic entropy relations,” Fortsch. Phys. 66, no.11-12, 1800067 (2018) [arXiv:1808.07871 [hep-th]]

    2018 arXiv

  20. [28]

    Holographic entropy cone for five regions,

    S. Hern´ andez Cuenca, “Holographic entropy cone for five regions,” Phys. Rev. D100, no.2, 026004 (2019) [arXiv:1903.09148 [hep-th]]

    2019 arXiv

  21. [29]

    Entanglement contour,

    G. Vidal and Y. Chen, “Entanglement contour,” J. Stat. Mech. 2014, no.10, P10011 (2014) [arXiv:1406.1471 [cond-mat.str-el]]

    2014 arXiv

  22. [30]

    Formulas for Partial Entanglement Entropy,

    Q. Wen, “Formulas for Partial Entanglement Entropy,” Phys. Rev. Res. 2, no.2, 023170 (2020) [arXiv:1910.10978 [hep-th]]

    2020 arXiv

  23. [31]

    Fine structure in holographic entanglement and entanglement contour,

    Q. Wen, “Fine structure in holographic entanglement and entanglement contour,” Phys. Rev. D 98, no.10, 106004 (2018) [arXiv:1803.05552 [hep-th]]

    2018 arXiv

  24. [32]

    Holographic entanglement contour, bit threads, and the entanglement tsunami,

    J. Kudler-Flam, I. MacCormack and S. Ryu, “Holographic entanglement contour, bit threads, and the entanglement tsunami,” J. Phys. A 52, no.32, 325401 (2019) [arXiv:1902.04654 [hep-th]]

    2019 arXiv

  25. [33]

    Bulk Locality and Quantum Error Correction in AdS/CFT,

    A. Almheiri, X. Dong and D. Harlow, “Bulk Locality and Quantum Error Correction in AdS/CFT,” JHEP 04, 163 (2015) [arXiv:1411.7041 [hep-th]]. 43

    2015 arXiv

  26. [34]

    Reconstruction of Bulk Operators within the Entanglement Wedge in Gauge-Gravity Duality,

    X. Dong, D. Harlow and A. C. Wall, “Reconstruction of Bulk Operators within the Entanglement Wedge in Gauge-Gravity Duality,” Phys. Rev. Lett. 117, no.2, 021601 (2016) [arXiv:1601.05416 [hep-th]]

    2016 arXiv

  27. [35]

    Holographic quantum error- correcting codes: Toy models for the bulk/boundary correspondence,

    F. Pastawski, B. Yoshida, D. Harlow and J. Preskill, “Holographic quantum error- correcting codes: Toy models for the bulk/boundary correspondence,” JHEP 06, 149 (2015) [arXiv:1503.06237 [hep-th]]

    2015 arXiv

  28. [36]

    Maximally multipartite entangled states,

    P. Facchi, G. Florio, G. Parisi and S. Pascazio, “Maximally multipartite entangled states,” Phys. Rev. A 77, no.6, 060304 (2008)

    2008

  29. [37]

    Absolute Maximal Entangle- ment and Quantum Secret Sharing,

    W. Helwig, W. Cui, A. Riera, J. I. Latorre and H. K. Lo, “Absolute Maximal Entangle- ment and Quantum Secret Sharing,” Phys. Rev. A86, 052335 (2012) [arXiv:1204.2289 [quant-ph]]

    2012 arXiv

  30. [38]

    Absolutely Maximally Entangled States: Existence and Applications,

    W. Helwig and W. Cui, “Absolutely Maximally Entangled States: Existence and Applications,” [arXiv:1306.2536 [quant-ph]]

    arXiv

  31. [39]

    Absolutely Maximally Entangled Qudit Graph States,

    W. Helwig, “Absolutely Maximally Entangled Qudit Graph States,” [arXiv:1306.2879 [quant-ph]]

    arXiv

  32. [40]

    Continuous Multiscale Entanglement Renormalization Ansatz as Holographic Surface-State Cor- respondence,

    M. Miyaji, T. Numasawa, N. Shiba, T. Takayanagi and K. Watanabe, “Continuous Multiscale Entanglement Renormalization Ansatz as Holographic Surface-State Cor- respondence,” Phys. Rev. Lett. 115, no.17, 171602 (2015) [arXiv:1506.01353 [hep-th]]

    2015 arXiv

  33. [41]

    Surface/State Correspondence as a Generalized Holog- raphy,

    M. Miyaji and T. Takayanagi, “Surface/State Correspondence as a Generalized Holog- raphy,” PTEP 2015, no.7, 073B03 (2015) [arXiv:1503.03542 [hep-th]]

    2015 arXiv

  34. [42]

    Tensor network decompositions for absolutely maxi- mally entangled states,

    B. Pozsgay and I. M. Wanless, “Tensor network decompositions for absolutely maxi- mally entangled states,” Quantum 8, 1339 (2024) [arXiv:2308.07042 [quant-ph]]

    2024 arXiv

  35. [43]

    Crossing Versus Locking: Bit Threads and Continuum Multiflows,

    M. Headrick, J. Held and J. Herman, “Crossing Versus Locking: Bit Threads and Continuum Multiflows,” Commun. Math. Phys. 396, no.1, 265-313 (2022) [arXiv:2008.03197 [hep-th]]

    2022 arXiv

  36. [44]

    Majorana dimers and holo- graphic quantum error-correcting codes,

    A. Jahn, M. Gluza, F. Pastawski and J. Eisert, “Majorana dimers and holo- graphic quantum error-correcting codes,” Phys. Rev. Research. 1, 033079 (2019) [arXiv:1905.03268 [hep-th]]

    2019 arXiv

  37. [45]

    Bidirectional holographic codes and sub-AdS locality,

    Z. Yang, P. Hayden and X. L. Qi, “Bidirectional holographic codes and sub-AdS locality,” JHEP 01, 175 (2016) [arXiv:1510.03784 [hep-th]]. 44

    2016 arXiv

  38. [46]

    Geodesic string condensation from symmetric tensor gauge theory: a unify- ing framework of holographic toy models,

    H. Yan, “Geodesic string condensation from symmetric tensor gauge theory: a unify- ing framework of holographic toy models,” Phys. Rev. B 102, no.16, 161119 (2020) [arXiv:1911.01007 [cond-mat.str-el]]

    2020 arXiv

  39. [47]

    Partial entanglement network and bulk geometry recon- struction in AdS/CFT,

    J. Lin, Y. Lu and Q. Wen, “Partial entanglement network and bulk geometry recon- struction in AdS/CFT,” [arXiv:2401.07471 [hep-th]]

  40. [48]

    Geometrizing the partial entanglement entropy: from PEE threads to bit threads,

    J. Lin, Y. Lu and Q. Wen, “Geometrizing the partial entanglement entropy: from PEE threads to bit threads,” JHEP 2024, no.02, 191 (2024) [arXiv:2311.02301 [hep-th]]

    2024 arXiv

  41. [49]

    Comments on Holographic Complexity,

    D. Carmi, R. C. Myers and P. Rath, “Comments on Holographic Complexity,” JHEP 03, 118 (2017) [arXiv:1612.00433 [hep-th]]

    2017 arXiv

  42. [50]

    Holographic Complexity,

    M. Alishahiha, “Holographic Complexity,” Phys. Rev. D 92, no.12, 126009 (2015) [arXiv:1509.06614 [hep-th]]

    2015 arXiv

  43. [51]

    Computational Complexity and Black Hole Horizons,

    L. Susskind, “Computational Complexity and Black Hole Horizons,” Fortsch. Phys. 64, 24-43 (2016) [arXiv:1403.5695 [hep-th]]

    2016 arXiv

  44. [52]

    Complexity and Shock Wave Geometries,

    D. Stanford and L. Susskind, “Complexity and Shock Wave Geometries,” Phys. Rev. D 90, no.12, 126007 (2014) [arXiv:1406.2678 [hep-th]]

    2014 arXiv

  45. [53]

    Holographic Complexity Equals Bulk Action?,

    A. R. Brown, D. A. Roberts, L. Susskind, B. Swingle and Y. Zhao, “Holographic Complexity Equals Bulk Action?,” Phys. Rev. Lett. 116, no.19, 191301 (2016) [arXiv:1509.07876 [hep-th]]

    2016 arXiv

  46. [54]

    Complexity, action, and black holes,

    A. R. Brown, D. A. Roberts, L. Susskind, B. Swingle and Y. Zhao, “Complexity, action, and black holes,” Phys. Rev. D 93, no.8, 086006 (2016) [arXiv:1512.04993 [hep-th]]

    2016 arXiv

  47. [55]

    Holographic Subregion Complexity from Kinematic Space,

    R. Abt, J. Erdmenger, M. Gerbershagen, C. M. Melby-Thompson and C. Northe, “Holographic Subregion Complexity from Kinematic Space,” JHEP 01, 012 (2019) [arXiv:1805.10298 [hep-th]]

    2019 arXiv

  48. [56]

    Topological Complexity in AdS 3/CFT2,

    R. Abt, J. Erdmenger, H. Hinrichsen, C. M. Melby-Thompson, R. Meyer, C. Northe and I. A. Reyes, “Topological Complexity in AdS 3/CFT2,” Fortsch. Phys. 66, no.6, 1800034 (2018) [arXiv:1710.01327 [hep-th]]

    2018 arXiv

  49. [57]

    Integral Geometry and Geometric Probability,

    L. A. Santal´o, “Integral Geometry and Geometric Probability,” Addison-Wesley Pub- lishing Company, Reading Massachusetts U.S.A. (1976). 45

    1976

  50. [58]

    Thread/State correspondence: from bit threads to qubit threads,

    Y. Y. Lin and J. C. Jin, “Thread/State correspondence: from bit threads to qubit threads,” JHEP 02, 245 (2023) [arXiv:2210.08783 [hep-th]]

    2023 arXiv

  51. [59]

    Thread/State correspondence: the qubit threads model of holographic gravity,

    Y. Y. Lin and J. C. Jin, “Thread/State correspondence: the qubit threads model of holographic gravity,” [arXiv:2208.08963 [hep-th]]

    arXiv

  52. [60]

    Exact and asymptotic measures of multipartite pure state entanglement,

    C. H. Bennett, S. Popescu, D. Rohrlich, J. A. Smolin, and A. V. Thapliyal, “Exact and asymptotic measures of multipartite pure state entanglement,” Phys. Rev. A 63(1):012307

  53. [61]

    Cali- brated Entanglement Entropy,

    I. Bakhmatov, N. S. Deger, J. Gutowski, E. ´O. Colg´ ain and H. Yavartanoo, “Cali- brated Entanglement Entropy,” JHEP 07, 117 (2017) [arXiv:1705.08319 [hep-th]]

    2017 arXiv

  54. [62]

    Geometric Aspects of Holographic Bit Threads,

    C. A. Ag´ on, J. De Boer and J. F. Pedraza, “Geometric Aspects of Holographic Bit Threads,” JHEP 05, 075 (2019) [arXiv:1811.08879 [hep-th]]

    2019 arXiv

  55. [63]

    Geometry of the (2+1) black hole,

    M. Banados, M. Henneaux, C. Teitelboim and J. Zanelli, “Geometry of the (2+1) black hole,” Phys. Rev. D 48, 1506-1525 (1993) [erratum: Phys. Rev. D 88, 069902 (2013)] [arXiv:gr-qc/9302012 [gr-qc]]

    1993 arXiv

  56. [64]

    New holographic generalization of entanglement entropy,

    Y. Nakata, T. Takayanagi, Y. Taki, K. Tamaoka and Z. Wei, “New holographic generalization of entanglement entropy,” Phys. Rev. D 103, no.2, 026005 (2021) [arXiv:2005.13801 [hep-th]]

    2021 arXiv

  57. [65]

    Timelike entanglement entropy,

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

    2023 arXiv

  58. [66]

    Lorentzian Threads as Gatelines and Holographic Complexity,

    J. F. Pedraza, A. Russo, A. Svesko and Z. Weller-Davies, “Lorentzian Threads as Gatelines and Holographic Complexity,” Phys. Rev. Lett. 127, no.27, 271602 (2021) [arXiv:2105.12735 [hep-th]]

    2021 arXiv

  59. [67]

    Sewing spacetime with Lorentzian threads: complexity and the emergence of time in quantum gravity,

    J. F. Pedraza, A. Russo, A. Svesko and Z. Weller-Davies, “Sewing spacetime with Lorentzian threads: complexity and the emergence of time in quantum gravity,” JHEP 02, 093 (2022) [arXiv:2106.12585 [hep-th]]

    2022 arXiv

  60. [68]

    Lorentzian threads and generalized complex- ity,

    E. Caceres, R. Carrasco and V. Patil, “Lorentzian threads and generalized complex- ity,” JHEP 04, 010 (2024) [arXiv:2312.10606 [hep-th]]

    2024 arXiv

  61. [69]

    Entanglement islands read perfect-tensor entan- glement,

    Y. Y. Lin, J. Zhang and J. C. Jin, “Entanglement islands read perfect-tensor entan- glement,” JHEP 04, 113 (2024) [arXiv:2312.14486 [hep-th]]. 46

    2024 arXiv

  62. [70]

    The PEE aspects of entanglement islands from bit threads,

    Y. Y. Lin, J. R. Sun, Y. Sun and J. C. Jin, “The PEE aspects of entanglement islands from bit threads,” JHEP 07, 009 (2022) [arXiv:2203.03111 [hep-th]]

    2022 arXiv

  63. [71]

    Partial entanglement entropy threads in the island phase,

    Q. Wen, M. Xu and H. Zhong, “Partial entanglement entropy threads in the island phase,” Phys. Rev. D 111, no.4, 046027 (2025) [arXiv:2408.13535 [hep-th]]

    2025 arXiv

  64. [72]

    Holographic definition of points and distances,

    B. Czech and L. Lamprou, “Holographic definition of points and distances,” Phys. Rev. D 90, 106005 (2014) [arXiv:1409.4473 [hep-th]]

    2014 arXiv

  65. [73]

    Holographic coarse-grained states and the necessity of perfect entanglement,

    Y. Y. Lin and J. Zhang, “Holographic coarse-grained states and the necessity of perfect entanglement,” Phys. Rev. D 109, no.12, 126012 (2024) [arXiv:2312.14498 [hep-th]]

    2024 arXiv

  66. [74]

    Bit thread, entanglement distillation, and entan- glement of purification,

    Y. Y. Lin, J. R. Sun and Y. Sun, “Bit thread, entanglement distillation, and entan- glement of purification,” Phys. Rev. D 103, no.12, 126002 (2021) [arXiv:2012.05737 [hep-th]]

    2021 arXiv

  67. [75]

    Tensor networks as conformal transformations,

    A. Milsted and G. Vidal, “Tensor networks as conformal transformations,” [arXiv:1805.12524 [cond-mat.str-el]]

    arXiv

  68. [76]

    Tensor networks as path integral geometry,

    A. Milsted and G. Vidal, “Tensor networks as path integral geometry,” [arXiv:1807.02501 [cond-mat.str-el]]

    arXiv

  69. [77]

    Geometric interpretation of the multi-scale entanglement renormalization ansatz,

    A. Milsted and G. Vidal, “Geometric interpretation of the multi-scale entanglement renormalization ansatz,” [arXiv:1812.00529 [hep-th]]

    arXiv

  70. [78]

    A holographic duality from lifted tensor networks,

    N. A. McMahon, S. Singh and G. K. Brennen, “A holographic duality from lifted tensor networks,” npj Quantum Inf. 6, 36 (2020) [arXiv:1812.11644 [cond-mat.str- el]]

    2020 arXiv

  71. [79]

    Hyperinvariant Tensor Networks and Holography,

    G. Evenbly, “Hyperinvariant Tensor Networks and Holography,” Phys. Rev. Lett. 119, no.14, 141602 (2017) [arXiv:1704.04229 [quant-ph]]

    2017 arXiv

  72. [80]

    Holographic duality from random tensor networks,

    P. Hayden, S. Nezami, X. L. Qi, N. Thomas, M. Walter and Z. Yang, “Holographic duality from random tensor networks,” JHEP 11, 009 (2016) [arXiv:1601.01694 [hep- th]]

    2016 arXiv

  73. [81]

    Space-time random tensor networks and holographic duality,

    X. L. Qi and Z. Yang, “Space-time random tensor networks and holographic duality,” [arXiv:1801.05289 [hep-th]]

    arXiv

  74. [82]

    Multipartite Entanglement in Stabilizer Tensor Networks,

    S. Nezami and M. Walter, “Multipartite Entanglement in Stabilizer Tensor Networks,” Phys. Rev. Lett. 125, 241602 (2020) [arXiv:1608.02595 [quant-ph]]. 47

    2020 arXiv

  75. [83]

    Tensor network and ( p-adic) AdS/CFT,

    A. Bhattacharyya, L. Y. Hung, Y. Lei and W. Li, “Tensor network and ( p-adic) AdS/CFT,” JHEP 01, 139 (2018) [arXiv:1703.05445 [hep-th]]

    2018 arXiv

  76. [84]

    p-adic CFT is a holographic tensor network,

    L. Y. Hung, W. Li and C. M. Melby-Thompson, “ p-adic CFT is a holographic tensor network,” JHEP 04, 170 (2019) [arXiv:1902.01411 [hep-th]]

    2019 arXiv

  77. [85]

    Emergent Einstein Equation in p-adic Confor- mal Field Theory Tensor Networks,

    L. Chen, X. Liu and L. Y. Hung, “Emergent Einstein Equation in p-adic Confor- mal Field Theory Tensor Networks,” Phys. Rev. Lett. 127, no.22, 221602 (2021) [arXiv:2102.12022 [hep-th]]

    2021 arXiv

  78. [86]

    Bending the Bruhat-Tits tree. Part I. Tensor network and emergent Einstein equations,

    L. Chen, X. Liu and L. Y. Hung, “Bending the Bruhat-Tits tree. Part I. Tensor network and emergent Einstein equations,” JHEP 06, 094 (2021) [arXiv:2102.12023 [hep-th]]

    2021 arXiv

  79. [87]

    Bending the Bruhat-Tits tree. Part II. The p-adic BTZ black hole and local diffeomorphism on the Bruhat-Tits tree,

    L. Chen, X. Liu and L. Y. Hung, “Bending the Bruhat-Tits tree. Part II. The p-adic BTZ black hole and local diffeomorphism on the Bruhat-Tits tree,” JHEP 09, 097 (2021) [arXiv:2102.12024 [hep-th]]

    2021 arXiv

  80. [88]

    CFT D from TQFTD+1 via Holographic Tensor Network, and Precision Discretisation of CFT 2,

    L. Chen, H. Zhang, K. Ji, C. Shen, R. Wang, X. Zeng and L. Y. Hung, “CFT D from TQFTD+1 via Holographic Tensor Network, and Precision Discretisation of CFT 2,” [arXiv:2210.12127 [hep-th]]

    arXiv

  81. [89]

    It from ETH: Multi-interval Entanglement and Replica Wormholes from Large-c BCFT Ensemble,

    H. Geng, L. Y. Hung and Y. Jiang, “It from ETH: Multi-interval Entanglement and Replica Wormholes from Large-c BCFT Ensemble,” [arXiv:2505.20385 [hep-th]]

    arXiv

  82. [90]

    Building up quantum spacetimes with BCFT Legos,

    L. Y. Hung and Y. Jiang, “Building up quantum spacetimes with BCFT Legos,” [arXiv:2404.00877 [hep-th]]

    arXiv

  83. [91]

    Group field theory and tensor networks: towards a Ryu–Takayanagi formula in full quantum gravity,

    G. Chirco, D. Oriti and M. Zhang, “Group field theory and tensor networks: towards a Ryu–Takayanagi formula in full quantum gravity,” Class. Quant. Grav. 35, no.11, 115011 (2018) [arXiv:1701.01383 [gr-qc]]

    2018 arXiv

  84. [92]

    Loop Quantum Gravity, Exact Holographic Mapping, and Holographic Entanglement Entropy,

    M. Han and L. Y. Hung, “Loop Quantum Gravity, Exact Holographic Mapping, and Holographic Entanglement Entropy,” Phys. Rev. D 95, no.2, 024011 (2017) [arXiv:1610.02134 [hep-th]]

    2017 arXiv

  85. [93]

    Holographic maps from quantum gravity states as tensor networks,

    E. Colafranceschi, G. Chirco and D. Oriti, “Holographic maps from quantum gravity states as tensor networks,” Phys. Rev. D 105, no.6, 066005 (2022) [arXiv:2105.06454 [hep-th]]. 48

    2022 arXiv

  86. [94]

    Holographic entanglement in spin network states: A focused review,

    E. Colafranceschi and G. Adesso, “Holographic entanglement in spin network states: A focused review,” A VS Quantum Sci.4, no.2, 025901 (2022) [arXiv:2202.05116 [hep- th]]

    2022 arXiv

  87. [95]

    Holographic spin networks from tensor network states,

    S. Singh, N. A. McMahon and G. K. Brennen, “Holographic spin networks from tensor network states,” Phys. Rev. D97, no.2, 026013 (2018) [arXiv:1702.00392 [cond- mat.str-el]]

    2018 arXiv

  88. [96]

    Tensor network state correspondence and holography,

    S. Singh, “Tensor network state correspondence and holography,” Phys. Rev. D 97, no.2, 026012 (2018) [arXiv:1701.04778 [cond-mat.str-el]]

    2018 arXiv

  89. [97]

    Beyond Toy Models: Distilling Tensor Networks in Full AdS/CFT,

    N. Bao, G. Penington, J. Sorce and A. C. Wall, “Beyond Toy Models: Distilling Tensor Networks in Full AdS/CFT,” JHEP 11, 069 (2019) [arXiv:1812.01171 [hep-th]]

    2019 arXiv

  90. [98]

    Surface growth scheme for bulk reconstruction and tensor network,

    Y. Y. Lin, J. R. Sun and Y. Sun, “Surface growth scheme for bulk reconstruction and tensor network,” JHEP 12, 083 (2020) [arXiv:2010.01907 [hep-th]]. 49

    2020 arXiv

Pith tools

Reviewed August 10, 2026 · model on record in the stance chip above.