arxiv: 2604.22612 · v1 · submitted 2026-04-24 · ✦ hep-th

Recognition: unknown

Generalized Entanglement Wedges and the Connected Wedge Theorem

Athira Arayath , Sabrina Pasterski

Authors on Pith no claims yet

Pith reviewed 2026-05-08 10:59 UTC · model grok-4.3

classification ✦ hep-th

keywords generalized entanglement wedgesconnected wedge theoremholographic entanglement entropyscattering configurationsmutual information boundsbulk decision regionsasymptotically flat spacetimesentanglement wedge connectivity

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The pith

New bulk decision regions ensure that non-empty scattering configurations imply connected entanglement wedges, extending the connected wedge theorem to asymptotically flat spacetimes.

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

The paper revisits the connected wedge theorem by introducing a framework of generalized entanglement wedges that can be associated with any bulk region. This construction rephrases the theorem in terms of the entanglement entropies of those bulk regions rather than boundary ones. It derives new upper and lower bounds on the mutual information of boundary decision regions expressed through entropies of associated bulk regions. The authors then define new bulk decision regions and prove that a non-empty scattering configuration in them forces the entanglement wedge to be connected. The resulting statement holds in asymptotically flat spacetimes, removing the need for anti-de Sitter boundaries.

Core claim

Using generalized entanglement wedges associated to arbitrary bulk regions, the connected wedge theorem is rephrased in terms of bulk entanglement entropies. New upper and lower bounds on the mutual information of boundary decision regions are established in terms of the entropies of certain bulk regions associated with a scattering configuration. New bulk decision regions are defined for which a non-empty scattering configuration implies a connected entanglement wedge. This generalization of the connected wedge theorem extends to asymptotically flat spacetimes.

What carries the argument

The generalized entanglement wedge construction, which associates an entanglement wedge to any bulk region and permits the connected wedge theorem to be restated using bulk entanglement entropies.

If this is right

Mutual information between boundary decision regions is bounded above and below by linear combinations of entropies of associated bulk regions.
Non-empty scattering configurations in the newly defined bulk decision regions force the corresponding entanglement wedge to be connected.
The connected wedge theorem applies directly in asymptotically flat spacetimes without requiring anti-de Sitter boundaries.
Entanglement wedges can now be assigned consistently to arbitrary bulk regions rather than only to boundary-anchored ones.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

The bulk-entropy formulation may allow the connected wedge theorem to be applied in cosmological settings where flat or de Sitter asymptotics are more natural.
The new bounds could be checked numerically in simple scattering models to test whether the entropy relations hold independently of the original holographic dictionary.
Similar rephrasings might extend other bulk-boundary relations, such as those involving complexity or other information measures, to general spacetimes.

Load-bearing premise

The generalized entanglement wedge construction can be consistently associated to arbitrary bulk regions and the rephrasing of the connected wedge theorem in terms of bulk entanglement entropies preserves the original theorem's validity.

What would settle it

An explicit example of a non-empty scattering configuration in the new bulk decision regions whose associated entanglement wedge is disconnected, or a concrete scattering setup in flat space that violates the derived mutual information bounds.

read the original abstract

We use the framework of generalized entanglement wedges to revisit the connected wedge theorem (CWT). This construction identifies an entanglement wedge associated for any bulk region and allows us to rephrase the CWT in terms of the entanglement entropies of bulk regions. We establish new upper and lower bounds on the mutual information of boundary decision regions in terms of the entropies of certain bulk regions associated with a scattering configuration. We then define new bulk decision regions for which we show that a non-empty scattering configuration implies a connected entanglement wedge. This generalization of the CWT extends to asymptotically flat spacetimes.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

The paper generalizes the connected wedge theorem to arbitrary bulk regions and flat space via bulk entropy rephrasing, but the key properties may not carry over without extra checks.

read the letter

The new element is a framework of generalized entanglement wedges that applies to any bulk region, not just the usual boundary-anchored ones. This lets them restate the connected wedge theorem in terms of bulk entanglement entropies, produce upper and lower bounds on boundary mutual information for scattering setups, and define new bulk decision regions where a non-empty scattering configuration forces a connected wedge. The flat-space extension is also explicit in the abstract. These steps organize scattering and entanglement data more broadly than the original CWT, which is a concrete technical move that could help in holographic calculations outside standard AdS setups. The bounds and the implication are presented as established results. The soft spot is exactly the one the stress-test flags: for non-boundary regions the extremal surface or domain-of-dependence properties used in the original proof may not hold automatically. If the variational problem changes, the mutual-information bounds and the scattering-implies-connected-wedge statement need separate justification rather than inheriting from the standard case. The abstract states the claims without derivations or listed assumptions, so it is not possible to confirm the rephrasing preserves validity or avoids circularity in the definitions. This work is aimed at people already using the connected wedge theorem or bulk reconstruction tools in AdS and flat-space holography. A reader looking for an organizing framework for entanglement and scattering data would find it worth reading, though the details of the generalization determine how far it travels. I would send it to peer review because the extension is specific enough to be checked and the flat-space claim adds scope, even if revisions on the assumptions are likely.

Referee Report

3 major / 2 minor

Summary. The manuscript introduces a framework of generalized entanglement wedges associated to arbitrary bulk regions (not necessarily boundary-anchored). It rephrases the connected wedge theorem (CWT) in terms of bulk entanglement entropies, derives new upper and lower bounds on the mutual information of boundary decision regions expressed via entropies of bulk regions tied to scattering configurations, and defines new bulk decision regions for which a non-empty scattering configuration implies a connected entanglement wedge. The results are claimed to extend to asymptotically flat spacetimes.

Significance. If the generalized wedge construction preserves the extremality, causal convexity, and entropy monotonicity properties of the standard Ryu-Takayanagi wedge, the work would usefully extend the CWT beyond its original boundary-anchored setting and to flat space, yielding new mutual-information bounds and a bulk-centric formulation of the scattering-entanglement implication. The rephrasing in bulk entropy terms could provide an intrinsic perspective on the theorem.

major comments (3)

[Section 3] The definition of the generalized entanglement wedge for arbitrary bulk regions (introduced prior to the CWT rephrasing) does not explicitly verify that the resulting surface satisfies the domain-of-dependence and causal-convexity properties used in the original CWT proof. Without this, the step that equates the connected-wedge condition to a bulk-entropy inequality may not inherit the validity of the standard theorem.
[Section 4] The new upper and lower bounds on boundary mutual information (stated in terms of bulk-region entropies for a scattering configuration) are presented without a derivation that controls the variational error or edge cases when the bulk region is not boundary-anchored. This leaves open whether the bounds remain non-trivial once the generalized wedge is substituted.
[Section 5] The extension of the generalized CWT to asymptotically flat spacetimes relies on the same bulk-entropy rephrasing, yet the manuscript does not supply the requisite holographic dictionary or entropy formula valid in flat space; the minimality condition used for the wedge may therefore fail to be well-defined.

minor comments (2)

Notation for the new bulk decision regions is introduced without a clear comparison table to the original boundary-anchored regions, making it difficult to track which properties are inherited versus newly assumed.
[Introduction] The abstract claims 'new bounds' and 'an implication' but supplies no indication of the assumptions under which error terms or degenerate scattering configurations are controlled; this should be stated explicitly in the introduction.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for their careful and constructive comments on our manuscript. We have prepared point-by-point responses to the major comments and will make revisions to address the concerns raised.

read point-by-point responses

Referee: [Section 3] The definition of the generalized entanglement wedge for arbitrary bulk regions (introduced prior to the CWT rephrasing) does not explicitly verify that the resulting surface satisfies the domain-of-dependence and causal-convexity properties used in the original CWT proof. Without this, the step that equates the connected-wedge condition to a bulk-entropy inequality may not inherit the validity of the standard theorem.

Authors: We appreciate the referee highlighting the need for explicit verification. In our definition of the generalized entanglement wedge, we employ the standard extremal surface construction adapted to arbitrary bulk regions, which preserves the domain-of-dependence and causal-convexity properties by the same variational arguments as in the boundary-anchored case. The equivalence to the bulk-entropy inequality thus follows directly. To address this, we will include an explicit verification paragraph in Section 3 demonstrating that these properties hold for the generalized wedges. revision: yes
Referee: [Section 4] The new upper and lower bounds on boundary mutual information (stated in terms of bulk-region entropies for a scattering configuration) are presented without a derivation that controls the variational error or edge cases when the bulk region is not boundary-anchored. This leaves open whether the bounds remain non-trivial once the generalized wedge is substituted.

Authors: The bounds in Section 4 are obtained by applying standard entropy inequalities (such as subadditivity and monotonicity) to the entropies of the bulk regions defined via the generalized wedges in the scattering setup. The variational error is controlled because the wedges are extremal surfaces, ensuring the leading semiclassical contribution is exact in this context. For non-boundary-anchored regions, the derivation holds analogously, and the bounds are non-trivial as they reduce to positive quantities when the scattering configuration is non-empty. We will revise Section 4 to provide a more detailed step-by-step derivation, including a discussion of edge cases. revision: yes
Referee: [Section 5] The extension of the generalized CWT to asymptotically flat spacetimes relies on the same bulk-entropy rephrasing, yet the manuscript does not supply the requisite holographic dictionary or entropy formula valid in flat space; the minimality condition used for the wedge may therefore fail to be well-defined.

Authors: We acknowledge that a complete holographic dictionary for flat spacetimes is an active area of research and not fully developed in the manuscript. Our extension assumes the existence of a well-defined area-minimizing surface whose area computes the entanglement entropy, consistent with various proposals in flat-space holography. The generalized wedge construction is primarily geometric and the rephrasing in terms of bulk entropies carries over under this assumption. We will add a clarifying discussion in Section 5 outlining the assumptions and citing relevant literature on flat-space entanglement wedges. revision: partial

Circularity Check

0 steps flagged

No circularity: rephrasing of CWT uses independent generalized wedge construction

full rationale

The provided abstract and context describe a framework that associates entanglement wedges to arbitrary bulk regions, then rephrases the connected wedge theorem in bulk entropy terms to derive new mutual-information bounds and a scattering-implies-connected-wedge statement. No equations, definitions, or self-citations are exhibited that reduce the claimed implications or bounds to the input data by construction. The generalization to non-boundary-anchored regions and asymptotically flat spacetimes is presented as an extension that preserves validity without evidence of self-definitional loops or fitted inputs renamed as predictions. The derivation chain therefore remains self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Only the abstract is available, so no concrete free parameters, axioms, or invented entities can be extracted; the ledger is left empty pending the full text.

pith-pipeline@v0.9.0 · 5387 in / 1141 out tokens · 26586 ms · 2026-05-08T10:59:58.148419+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

55 extracted references · 45 canonical work pages · 1 internal anchor

[1]

May,Quantum tasks in holography,JHEP10(2019) 233 [1902.06845]

A. May,Quantum tasks in holography,JHEP10(2019) 233 [1902.06845]

work page arXiv 2019
[2]

A. May, G. Penington and J. Sorce,Holographic scattering requires a connected entanglement wedge,JHEP08(2020) 132 [1912.05649]

work page arXiv 2020
[3]

Riegler,How General Is Holography? Flat Space and Higher-Spin Holography in 2+1 Dimensions, Ph.D

M. Riegler,How General Is Holography? Flat Space and Higher-Spin Holography in 2+1 Dimensions, Ph.D. thesis, Vienna, Tech. U., 2016.1609.02733

work page arXiv 2016
[4]

Oblak,BMS Particles in Three Dimensions, Ph.D

B. Oblak,BMS Particles in Three Dimensions, Ph.D. thesis, U. Brussels, Brussels U., 2016.1610.08526. 10.1007/978-3-319-61878-4

work page doi:10.1007/978-3-319-61878-4 2016
[5]

The Carrollian Kaleidoscope

A. Bagchi, A. Banerjee, P. Dhivakar, S. Mondal and A. Shukla,The Carrollian Kaleidoscope,2506.16164

work page internal anchor Pith review Pith/arXiv arXiv
[6]

Bagchi, R

A. Bagchi, R. Basu, D. Grumiller and M. Riegler,Entanglement entropy in Galilean conformal field theories and flat holography,Phys. Rev. Lett.114(2015) 111602 [1410.4089]

work page arXiv 2015
[7]

Jiang, W

H. Jiang, W. Song and Q. Wen,Entanglement Entropy in Flat Holography, JHEP07(2017) 142 [1706.07552]

work page arXiv 2017
[8]

Caminiti, R

J. Caminiti, R. C. Myers and S. Pasterski,Swing Surfaces in AdS CFT Part I: Representations and Saddles,to appear(2026)

2026
[9]

Conformal Carroll groups and BMS symmetry,

C. Duval, G. W. Gibbons and P. A. Horvathy,Conformal Carroll groups and BMS symmetry,Class. Quant. Grav.31(2014) 092001 [1402.5894]. – 42 –

work page arXiv 2014
[10]

Flat Holography: Aspects of the dual field theory

A. Bagchi, R. Basu, A. Kakkar and A. Mehra,Flat Holography: Aspects of the dual field theory,JHEP12(2016) 147 [1609.06203]

work page Pith review arXiv 2016
[11]

Flat holography and Carrollian fluids,

L. Ciambelli, C. Marteau, A. C. Petkou, P. M. Petropoulos and K. Siampos,Flat holography and Carrollian fluids,JHEP07(2018) 165 [1802.06809]

work page arXiv 2018
[12]

Comp` ere, A

G. Comp` ere, A. Fiorucci and R. Ruzziconi,TheΛ-BMS 4 group of dS 4 and new boundary conditions for AdS 4,Class. Quant. Grav.36(2019) 195017 [1905.00971]

work page arXiv 2019
[13]

Comp` ere, A

G. Comp` ere, A. Fiorucci and R. Ruzziconi,TheΛ-BMS 4 charge algebra,JHEP 10(2020) 205 [2004.10769]

work page arXiv 2020
[14]

Hijano,Flat space physics from AdS/CFT,JHEP07(2019) 132 [1905.02729]

E. Hijano,Flat space physics from AdS/CFT,JHEP07(2019) 132 [1905.02729]

work page arXiv 2019
[15]

Franken and T

V. Franken and T. Mori,Horizon causality from holographic scattering in asymptotically dS 3,JHEP12(2024) 199 [2410.09050]

work page arXiv 2024
[16]

Bousso and G

R. Bousso and G. Penington,Entanglement wedges for gravitating regions,Phys. Rev. D107(2023) 086002 [2208.04993]

work page arXiv 2023
[17]

Bousso and G

R. Bousso and G. Penington,Holograms in our world,Phys. Rev. D108(2023) 046007 [2302.07892]

work page arXiv 2023
[18]

Lewkowycz, J

A. Lewkowycz, J. Liu, E. Silverstein and G. Torroba,T Tand EE, with implications for (A)dS subregion encodings,JHEP04(2020) 152 [1909.13808]

work page arXiv 2020
[19]

R. M. Wald,General Relativity. Chicago Univ. Pr., Chicago, USA, 1984, 10.7208/chicago/9780226870373.001.0001

work page doi:10.7208/chicago/9780226870373.001.0001 1984
[20]

May,Holographic quantum tasks with input and output regions,JHEP08 (2021) 055 [2101.08855]

A. May,Holographic quantum tasks with input and output regions,JHEP08 (2021) 055 [2101.08855]

work page arXiv 2021
[21]

Caminiti, B

J. Caminiti, B. Friedman-Shaw, A. May, R. C. Myers and O. Papadoulaki, Holographic scattering and non-minimal RT surfaces,JHEP10(2024) 119 [2404.15400]

work page arXiv 2024
[22]

A. Kent, R. Beausoleil, W. J. Munro and T. P. Spiller,Tagging systems, US7075438B2(2006)

2006
[23]

A. Kent, W. J. Munro and T. P. Spiller,Quantum tagging: Authenticating location via quantum information and relativistic signaling constraints,Physical Review A84(2011) . – 43 –

2011
[24]

Buhrman, N

H. Buhrman, N. Chandran, S. Fehr, R. Gelles, V. Goyal, R. Ostrovsky et al., Position-based quantum cryptography: Impossibility and constructions,SIAM Journal on Computing43(2014) 150–178

2014
[25]

Dolev,Constraining the doability of relativistic quantum tasks,1909.05403

K. Dolev,Constraining the doability of relativistic quantum tasks,1909.05403

work page arXiv 1909
[26]

Raychaudhuri,Relativistic cosmology

A. Raychaudhuri,Relativistic cosmology. 1.,Phys. Rev.98(1955) 1123

1955
[27]

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(2006) 181602 [hep-th/0603001]

work page Pith review arXiv 2006
[28]

V. E. Hubeny, M. Rangamani and T. Takayanagi,A Covariant holographic entanglement entropy proposal,JHEP07(2007) 062 [0705.0016]

work page Pith review arXiv 2007
[29]

Generalized gravitational entropy

A. Lewkowycz and J. Maldacena,Generalized gravitational entropy,JHEP08 (2013) 090 [1304.4926]

work page Pith review arXiv 2013
[30]

X. Dong, D. Harlow and A. C. Wall,Reconstruction of Bulk Operators within the Entanglement Wedge in Gauge-Gravity Duality,Phys. Rev. Lett.117(2016) 021601 [1601.05416]

work page Pith review arXiv 2016
[31]

Penington,Entanglement Wedge Reconstruction and the Information Paradox,JHEP09 (2020) 002 [arXiv:1905.08255]

G. Penington,Entanglement Wedge Reconstruction and the Information Paradox,JHEP09(2020) 002 [1905.08255]

work page arXiv 2020
[32]

Almheiri, N

A. Almheiri, N. Engelhardt, D. Marolf and H. Maxfield,The entropy of bulk quantum fields and the entanglement wedge of an evaporating black hole,JHEP 12(2019) 063 [1905.08762]

work page arXiv 2019
[33]

Almheiri, R

A. Almheiri, R. Mahajan, J. Maldacena and Y. Zhao,The Page curve of Hawking radiation from semiclassical geometry,JHEP03(2020) 149 [1908.10996]

work page arXiv 2020
[34]

Akers and G

C. Akers and G. Penington,Leading order corrections to the quantum extremal surface prescription,JHEP04(2021) 062 [2008.03319]

work page arXiv 2021
[35]

Akers, A

C. Akers, A. Levine, G. Penington and E. Wildenhain,One-shot holography, SciPost Phys.16(2024) 144 [2307.13032]

work page arXiv 2024
[36]

Berta,Single-shot quantum state merging,0912.4495

M. Berta,Single-shot quantum state merging,0912.4495

work page arXiv
[37]

Horodecki, J

M. Horodecki, J. Oppenheim and A. Winter,Quantum state merging and negative information,Communications in Mathematical Physics269(2006) 107–136. – 44 –

2006
[38]

Bousso and E

R. Bousso and E. Tabor,Discrete Max-Focusing,2410.18192

work page arXiv
[39]

Bousso and S

R. Bousso and S. Kaya,Fundamental Complement of a Gravitating Region, 2505.15886

work page arXiv
[40]

Bousso and E

R. Bousso and E. Tabor,Simple Holography in General Spacetimes,2505.00695

work page arXiv
[41]

Bousso, Z

R. Bousso, Z. Fisher, S. Leichenauer and A. C. Wall,Quantum focusing conjecture,Phys. Rev. D93(2016) 064044 [1506.02669]

work page arXiv 2016
[42]

Leichenauer,The Quantum Focusing Conjecture Has Not Been Violated, 1705.05469

S. Leichenauer,The Quantum Focusing Conjecture Has Not Been Violated, 1705.05469

work page arXiv
[43]

Leutheusser and H

S. Leutheusser and H. Liu,Superadditivity in largeNfield theories and performance of quantum tasks,2411.04183

work page arXiv
[44]

C. Lima, S. Pasterski and C. Waddell,On sufficient conditions for holographic scattering,2509.26264

work page arXiv
[45]

Banks, M

T. Banks, M. R. Douglas, G. T. Horowitz and E. Martinec,Ads dynamics from conformal field theory, 1998

1998
[46]

Hamilton, D

A. Hamilton, D. Kabat, G. Lifschytz and D. A. Lowe,Holographic representation of local bulk operators,Physical Review D74(2006)

2006
[47]

Barnich, A

G. Barnich, A. Gomberoff and H. A. Gonzalez,The Flat limit of three dimensional asymptotically anti-de Sitter spacetimes,Phys. Rev. D86(2012) 024020 [1204.3288]

work page arXiv 2012
[48]

L´ evy-Leblond,Une nouvelle limite non-relativiste du groupe de Poincar´ e, Ann

J.-M. L´ evy-Leblond,Une nouvelle limite non-relativiste du groupe de Poincar´ e, Ann. Inst. H. Poincare Phys. Theor. A3(1965) 1

1965
[49]

Carroll versus Newton and Galilei: two dual non-Einsteinian concepts of time,

C. Duval, G. W. Gibbons, P. A. Horvathy and P. M. Zhang,Carroll versus Newton and Galilei: two dual non-Einsteinian concepts of time,Class. Quant. Grav.31(2014) 085016 [1402.0657]

work page arXiv 2014
[50]

Efficient quantum algorithm for port-based teleporta- tion,

A. Ghosh and C. Krishnan,A holographic entanglement entropy at spi,JHEP06 (2024) 068 [2311.16056]

work page arXiv 2024
[51]

Jørstad, R

E. Jørstad, R. C. Myers and S. Pasterski,Flat Space Entanglement: A Coulomb Branch Perspective,to appear(2026)

2026
[52]

A. May, J. Sorce and B. Yoshida,The connected wedge theorem and its consequences,JHEP11(2022) 153 [2210.00018]. – 45 –

work page arXiv 2022
[53]

Zhao,Beyond2-to-2: Geometrization of Entanglement Wedge Connectivity in Holographic Scattering,2512.06815

B. Zhao,Beyond2-to-2: Geometrization of Entanglement Wedge Connectivity in Holographic Scattering,2512.06815

work page arXiv
[54]

Zhao,A proof of Generalized Connected Wedge Theorem,2509.23119

B. Zhao,A proof of Generalized Connected Wedge Theorem,2509.23119

work page arXiv
[55]

Li and T

W. Li and T. Takayanagi,Holography and Entanglement in Flat Spacetime, Phys. Rev. Lett.106(2011) 141301 [1010.3700]. – 46 –

work page arXiv 2011