Pith. sign in

REVIEW 4 major objections 5 minor 2 cited by

Measurements $\mathit{with}$ probabilities in the final state proposal

T0 review · 4 major / 5 minor · reviewed 2026-08-07 · deepseek-v4-flash

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

Pith's one-line read The final state proposal recovers well-defined probabilities for the AMPS experiment when the second measurement is aimed at the interior created by the first measurement's distillation operator rather than the original interior.

desk verdict A genuinely new diagnosis of the Bousso-Stanford flaw, but the resolution rests on a prescription for choosing the interior that is asserted, not derived. read the letter →

arxiv 2505.23664 v2 pith:OX4LFS5R submitted 2025-05-29 hep-th gr-qc

Ahmed Almheiri This is my paper
classification hep-thgr-qc
keywords blackholefinalstateAMPSexperimentdecoherencefunctionalentanglementwedgereconstructionreplicawormholesnon-isometriccodesrandommodelacausality
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

An earlier analysis concluded that the black hole final state proposal breaks down for the full AMPS experiment: the second measurement's outcomes have no probabilities, and the first measurement's statistics depend on future choices. This paper argues that the conclusion rests on a wrong choice of which black hole interior the second measurement probes. After the first AMPS measurement, the distillation operator introduces several candidate interiors; the physical one, the paper argues, is the interior on the time-symmetric slice of the dominant saddle in the state's norm. Using that rule in a random final state model, the decoherence functional is diagonal with the only nonzero component $D^{(1,1)}_{(1,1)}=1$, so both measurements succeed with certainty and the acausality disappears. The paper therefore defends the final state proposal against the earlier objections.

What carries the argument

The central object is the distillation operator $D_E$, a Petz-Lite map obtained by tracing a code-space distillation operator over the black hole degrees of freedom; it is a non-isometric tensor that acts on the radiation and produces a distilled mode $e_b$ entangled with $b$. The load-bearing selection rule is that the physical interior is the one intersected by the time-symmetric slice of the dominant unitary contraction in the Haar-averaged norm of the measured state. This rule converts the multiple interiors left by the first measurement into a unique answer, and it is what makes the decoherence functional diagonal.

What would settle it

Perform the Haar average of the full AMPS decoherence functional with the second measurement directed at each of the four candidate interiors introduced by the distillation; the paper predicts the diagonal form only for the interior on the dominant time-symmetric slice, so any other interior yielding a diagonal functional would contradict the selection rule, while the original interior reproducing the off-diagonal result would confirm it.

Watch

Extended reading notes

Core claim

Working in a generalization of Lloyd's random final state model built from non-isometric codes, the paper computes the decoherence functional for the two-step AMPS experiment. It finds that once the first measurement is implemented with the distillation operator $D_E$, the second measurement must be directed at the interior that the distiller itself introduces, not the original interior. With that choice the only nonzero component of the decoherence functional is $D^{(1,1)}_{(1,1)}=1$ to exponential accuracy: measurement (I) succeeds because $b$ is maximally entangled with the distilled mode $e_b$, and measurement (II) succeeds because $b$ is purified by its interior partner. The off-diagonal components and acausal dependence on future measurements arise, in this model, from applying the second measurement to the original interior, which the paper argues is inconsistent with entanglement wedge reconstruction and with how operators change states.

Load-bearing premise

The result depends on identifying the physical interior after the first measurement as the one singled out by the dominant saddle in the norm of the measured state; if another interior is chosen, or if subleading saddles contribute, the ill-defined probabilities and acausal behavior return.

Editorial extensions

If this is right

  • If the paper is right, the AMPS experiment is compatible with both unitarity, via $b$ entangled with early radiation, and a smooth horizon, via $b$ purified by its interior partner, with no acausal dependence of measurement (I) on measurement (II).
  • The earlier difficulties are not a general feature of final state models but an artifact of choosing the wrong interior; a corrected implementation removes them.
  • The final state proposal remains viable as a resolution of the information and firewall paradoxes, at least at the level of this toy model.
  • The diagonal decoherence functional implies the two measurements' outcomes are perfectly correlated, so the experiment cannot be used to exhibit a firewall.
  • The prescription gives a concrete, computable rule for which interior an infalling observer encounters after operations on the radiation.

Reading between the lines

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

  • The paper's selection rule, if correct, implies that any non-semiclassical operation on the radiation, not just distillation, should dictate which interior an infalling observer probes; this gives a testable organizing principle for other final state or island models.
  • The diagonal decoherence functional suggests that the final state proposal may assign well-defined probabilities to arbitrary sequences of measurements, making the earlier obstruction a special case of misdirecting the later measurement rather than a generic failure.
  • A full gravitational version of the argument would need to establish the same saddle dominance beyond the Haar-random toy model; until then, the 100% certainty is a property of this model class, not yet of semiclassical gravity.
  • The paper explicitly sets aside the exponential time needed to implement distillation unitarily, so if no proposed workaround exists, the experiment's certainty is formal rather than physically realizable.
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. This paper revisits the Bousso-Stanford (BS) analysis of the AMPS experiment in the black-hole final-state proposal and claims to identify a loophole. Working in a finite-dimensional random final-state model based on non-isometric codes, the author argues that the first AMPS measurement, which requires distilling a mode from the early radiation, introduces multiple candidate black-hole interiors. A prescription is then proposed: after the first measurement, the physical interior is the one selected by the dominant contribution to the norm of the measured state, specifically the 'last unitary' in the distillation operator. With this rule, the author claims that the decoherence functional for the full AMPS experiment is diagonal, with the only nonzero component D^(1,1)_(1,1)=1 to exponential accuracy, so both measurements succeed with certainty and the BS problems of ill-defined probabilities and acausality disappear. The BS implementation is instead traced to the choice of the original black-hole interior for the second measurement. The paper is a letter whose central steps are presented diagrammatically and asserted rather than derived.

Significance. If the central claims could be substantiated, this would be an important resolution of the BS objections to the final-state proposal and a concrete illustration of how entanglement-wedge reconstruction and replica-wormhole intuition affect post-selected measurements. The manuscript is conceptually clear, and the finite-dimensional random-model setup is an appropriate arena for the question. The paper also identifies a genuinely interesting physical issue: the distillation step in the first AMPS measurement changes the spacetime, so the location of the second measurement is not automatically the original interior. The main weakness is that the decisive steps—the delta-function identity for the projected states, the dominance of a particular saddle, and the exponential accuracy—are asserted through diagrams rather than computed. As it stands, the diagonal decoherence functional is a consequence of an interior-selection prescription, not an independently demonstrated property of the model.

major comments (4)
  1. [AMPS experiment with a final state (between Eqs. (8) and (9))] The identity |Π(m,n)Ψ⟩ = δmn|Π(n,n)Ψ⟩ is the central result of the paper, but it is asserted rather than derived. The text says it is 'very straightforward' because the two measurements occur sequentially on the same systems, yet in the diagrammatic setup the second measurement acts on a Hilbert-space factor that is identified with the interior only by the preceding selection rule. The paper should present the explicit Haar integral for ⟨Π(m',n')Ψ|Π(m,n)Ψ⟩, including all contractions, and show that the off-diagonal terms vanish or are exponentially suppressed after normalization by ⟨Ψ|Ψ⟩. Without this calculation, the diagonal decoherence functional is a restatement of the prescription, not a prediction of the random final-state model.
  2. [AMPS experiment with a final state (paragraph after Eq. (8))] The interior-selection rule is introduced without quantitative justification. The statement that 'in the dominant contribution to the norm, the unitary contractions follow early radiation contractions, and therefore only the last unitary in the first AMPS measurement (sage) will intersect the time symmetric slice' is a claim about which saddle dominates, but no computation of the relative weights of the possible contractions is shown. The paper should specify the large-dimension hierarchy (for example, E ≫ M/E ≫ b) and demonstrate with explicit powers of 1/E or 1/b that all other contractions are subleading, both in the norm of the measured state and in the decoherence functional. If a subleading saddle contributed at the relevant order, or if a different interior were selected, the off-diagonal components would reappear and the BS problems would return.
  3. [AMPS experiment with a final state (paragraph after Eq. (9))] The statement 'since the distiller successfully distills, we have δmn|Π(n,n)Ψ⟩ ≈ δmnδn1|Π(1,1)Ψ⟩ ≈ δmnδn1|Ψ⟩ to exponential accuracy' is an input assumption rather than a derived result. The distillation operator D_E is defined through Eqs. (4)-(6) so that its action produces the distilled state; the fact that the second measurement then finds the distilled mode with probability one is definitional once the physical interior is declared to be the one created by D_E. The paper should separate this definitional success from the nontrivial claim that the probability is one after including all saddles and after normalizing by ⟨Ψ|Ψ⟩. The current text conflates the construction of D_E with the computation of the decoherence functional.
  4. [AMPS experiment, the BS version (after Eq. (12))] The BS version is not actually evaluated. The paper states that 'Evaluating this reproduces the decoherence functional of BS [8]' but provides no expression for the off-diagonal components or for the acausal correlations. Since the paper's main contrast is between D^(1,1)_(1,1)=1 and BS's non-diagonal functional, a derivation of Eq. (12), or at least the leading nonzero components of the Haar-averaged decoherence functional, is needed to substantiate the comparison and to show that the 'crisscrossed' diagram indeed gives the BS result. Without this, the claim that the BS difficulties are due to a wrong choice of interior is not established.
minor comments (5)
  1. [Title] The title string in the manuscript text appears as 'Measurements ((((( hhhhhwithout with probabilities in the final state proposal', which is garbled; the intended title should be cleaned to 'Measurements with probabilities in the final state proposal'.
  2. [Footnote 7] Footnote 7 contains unresolved placeholders 'timefold [?]' and 'the claim in [ ? ]'; these citations need to be completed.
  3. [Notation for Eqs. (9) and (10)] The same notation |Π(m,n)Ψ⟩ is used for the author's version in Eq. (9) and for the BS version in Eq. (10), although these are different states defined by different time orderings of the projectors. A distinguishing notation or an explicit verbal reminder would avoid confusion.
  4. [Paragraph after Eq. (9)] The sentence 'For simplicity, the projection of ˜bb is implemented without dropping b into the black hole' would benefit from a justification of why this simplification is equivalent to the physical AMPS experiment, where the observer carries b through the horizon.
  5. [Dimension hierarchy after Eq. (1)] The expression 'E ≫ M/E ≫ b' is dimensionally confusing because M and E are Hilbert-space dimensions. Please clarify that these are ratios of dimensions (for example, dim E ≫ dim M / dim E ≫ dim b) and state the large parameters used for the exponential accuracy estimates.

Circularity Check

3 steps flagged · score 6.0 of 10

Diagonal decoherence functional and 100% AMPS success reduce by construction to the paper's interior-selection prescription and to the distiller's defining property; the sage-contraction dominance is asserted rather than derived.

  1. self definitional [Section 'AMPS experiment with a final state', paragraph beginning 'In contrast to the first AMPS measurement' (after Eq. (8))]
    "We already encountered this problem when analyzing the distiller; the true black hole interior belongs to the spacetime described by the state following the distillation, i.e. the dominant contribution to the norm of the state. Similarly, we are interested in observations of the black hole in the dominant contribution to the norm of the measured state."

    The 'measured state' |Π(n)Ψ⟩ ≡ Ξ(n)⟨F|U|...⟩ already contains the first AMPS measurement and its outcome n. Defining the 'physical' interior as the dominant contribution to the norm of this state is what selects the distiller's last unitary ('sage') and hence identifies the mode probed in the second measurement with the distilled mode eb. The later claim that the second measurement confirms the first is therefore not deduced from the final-state model; it is written into the definition of which interior is physical. BS's competing rule—using the original interior, Eq. (10)—would produce the off-diagonal decoherence functional of Eq. (12), confirming that the diagonal result depends entirely on this choice.

  2. self definitional [Section 'AMPS experiment with a final state', after Eq. (9), before the decoherence functional definition]
    "Since the two measurements occur sequentially on the same systems, their results must match, and so |Π(m,n)Ψ⟩ = δmn|Π(n,n)Ψ⟩."

    The identity says the two sequential AMPS measurements must agree because they act 'on the same systems'. This is exactly the content of the preceding selection rule: the physical \tilde b was set equal to the distilled eb, so Π(m) on \tilde b b and Π(n) on beb are projections onto the same pair of modes (up to relabeling). Applied twice, the same projector gives δmn by elementary algebra. Without that identification, as in the BS implementation, the two measurements act on different interiors and the overlap is not diagonal. The δmn identity is thus a restatement of the interior-selection prescription, not an independent property of the random final state model.

1 more flagged steps
  1. fitted input called prediction [Section 'AMPS experiment with a final state', same paragraph after the δmn identity]
    "Moreover, since the distiller successfully distills, we have δmn|Π(n,n)Ψ⟩ ≈ δmnδn1|Π(1,1)Ψ⟩ ≈ δmnδn1|Ψ⟩ to exponential accuracy (averaging over the final state is implicit)."

    The success of the distillation ('the distiller successfully distills') is the defining property of the operator DE: in Eq. (6) it was constructed so that Dcode maps the code subspace to states where eb is distilled, and the paper earlier states 'the distilled mode eb is nothing but ˜b from the black hole interior ... in the bra'. Using this input to conclude δn1, and then announcing 'both AMPS measurements succeed with 100% certainty', relabels the construction as a measurement outcome. The 100% certainty claim is therefore forced by the definition of DE plus the same-systems identification; no independent probability computation is shown.

full rationale

Most of the technical machinery—the random final state model, the Haar-averaged overlap in Eq. (7), the diagrammatics of DE, and the contrast with BS—is independent and internally coherent. The central claim that the two AMPS measurements always agree (D(1,1)_(1,1)=1) nonetheless reduces by construction to two inputs. First, the physical interior for the second measurement is defined as the one intersecting the time-symmetric slice of the dominant contribution to the norm of the state after the first measurement, i.e., the 'sage' interior introduced by the distiller; this directly identifies the second-measurement mode with the distilled mode eb. Second, 'the distiller successfully distills' is the defining property of the Petz-Lite operator DE, and is used to set δn1. With these inputs, |Π(m,n)Ψ⟩ = δmn|Π(n,n)Ψ⟩ is the trivial identity that successive projections on the same pair of modes agree; it is not an output of the final-state model. The paper is explicit that the interior choice is a 'prescription', and it shows that BS's alternative choice (Eq. (10)) would give off-diagonal D, which confirms that the result is contingent on the prescription rather than derived from the model alone. The additional assertion that 'only the last unitary ... will intersect the time symmetric slice' is not demonstrated in the text; even if it were, the diagonal decoherence functional would still follow almost entirely from the same-systems identification. No load-bearing self-citation chain is involved; the papers cited for replica-wormhole insights are external support. Score 6: the paper's headline prediction is substantially constructed, though the model framework and the BS critique retain independent content.

Assumptions & free parameters 0 free parameters · 4 assumptions · 1 invented entities

The central claim rests on a specific toy model (Haar-random final state), a selection rule for which interior is physical, and an assumed successful distillation; none of these are derived from gravity or from the original final state proposal, and none are externally falsifiable within the paper.

assumptions (4)
  • domain assumption A partially projected Haar-random unitary (or K-design) with the stated dimensions captures the physics of the black hole final state and mimics replica wormhole contractions after averaging.
    The model is introduced in the section 'A not so final final state' and motivated by Stanford's observation [25] of similarity between replica wormholes and Weingarten contractions; it is not derived from a gravitational path integral.
  • ad hoc to paper The physical interior probed after the first AMPS measurement is the one selected by the dominant contribution to the norm of the measured state, specifically the last unitary in the distillation operator.
    This selection rule is stated in the section 'AMPS experiment with a final state' and is the mechanism that makes the decoherence functional diagonal; it is not proven from first principles.
  • domain assumption The Petz-Lite operator DE implements distillation with unit success in the code subspace, so after the first AMPS measurement the state is, to exponential accuracy, the original state |Ψ⟩ with b purified by the distilled mode eb.
    The paper asserts 'since the distiller successfully distills' and uses this to collapse the decoherence functional to δn1; the finite-N success probability is not computed.
  • ad hoc to paper The AMPS observer can implement the distillation despite the Harlow-Hayden exponential complexity bound.
    Footnote 8 acknowledges the computational obstruction and assumes a workaround from references [31,32]; the central consistency result depends on this feasibility.
invented entities (1)
  • Distiller-created black hole interior (interior I)
    purpose: Acts as the true location of the second AMPS measurement after the first measurement distills eb from the radiation.
    The paper introduces this interior in Fig 2 and the diagram around Eq (7), selected by the dominant saddle; no independent observable distinguishes it from the original interior, so it is an invented conceptual entity without an external falsifiable handle.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Measurements $\mathit{with}$ probabilities in the final state proposal." pith.science (2026). https://pith.science/paper/OX4LFS5R

@misc{pith2026250523664,
  author       = {Pith},
  title        = {Pith review of: Measurements $\mathitwith$ probabilities in the final state proposal},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/OX4LFS5R}},
  note         = {Machine review of arXiv:2505.23664}
}
read the original abstract

Bousso and Stanford (BS) argued that the black hole final state proposal leads to acausal effects and ill-defined probabilities for the AMPS experiment. We identify a loophole in their analysis using insights from entanglement wedge reconstruction and replica wormholes. We trace the cause of the BS problems to the misidentification of the physical interior where the second AMPS measurement happens from among the multiple interiors introduced by the first measurement.

Figures

Figures reproduced from arXiv: 2505.23664 by the authors.

Figure 1
Figure 1. FIG. 1 [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. Acting on the original black hole radiation system [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗

Discussion (0). Sign in to comment.

Forward citations

Cited by 2 Pith papers

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

  1. Observer complementarity for black holes and holography

    hep-th 2025-07 conditional novelty 7.0 of 10

    The authors show that the observer rule of Harlow, Usatyuk, and Zhao yields a self-consistent black hole complementarity for both partially and fully evaporated black holes.

  2. The Baby Universe is Fine and the CFT Knows It: On Holography for Closed Universes

    hep-th 2025-07 conditional novelty 5.0 of 10

    A closed universe in AdS/CFT is not ruled out by recent SWAP-test arguments; the one-dimensional Hilbert space seen from the CFT is external indistinguishability, and CFT data can reconstruct the closed universe's geometry.

Reference graph

Works this paper leans on

35 extracted references · 8 canonical work pages · cited by 2 Pith papers

  1. [8]

    Bousso and D

    R. Bousso and D. Stanford, Measurements without Probabilities in the Final State Proposal, Phys. Rev. D 89, 044038, 2014, [arXiv:1310.7457 [hep-th]]

    arXiv 2014

  2. [1]

    G. T. Horowitz and J. M. Maldacena, The Black hole final state, JHEP 02, 008, 2004, [arXiv:hep-th/0310281]

    arXiv 2004

  3. [2]

    S. W. Hawking, Breakdown of Predictability in Gravitational Collapse, Phys. Rev. D 14, 2460–2473, 1976

    work page 1976

  4. [3]

    Almheiri, D

    A. Almheiri, D. Marolf, J. Polchinski and J. Sully, Black Holes: Complementarity or Firewalls?, JHEP 02, 062, 2013, [arXiv:1207.3123 [hep-th]]

    arXiv 2013

  5. [4]

    C. H. Bennett, G. Brassard, C. Crepeau, R. Jozsa, A. Peres and W. K. Wootters, Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels, Phys. Rev. Lett. 70, 1895–1899, 1993

    work page 1993

  6. [5]

    S. L. Braunstein, S. Pirandola and K. ˙Zyczkowski, Better Late than Never: Information Retrieval from Black Holes, Phys. Rev. Lett. 110, 101301, 2013, [arXiv:0907.1190 [quant-ph]]

    arXiv 2013

  7. [6]

    S. D. Mathur, The Information paradox: A Pedagogical introduction, Class. Quant. Grav. 26, 224001, 2009, [arXiv:0909.1038 [hep-th]]

    arXiv 2009

  8. [7]

    Lloyd and J

    S. Lloyd and J. Preskill, Unitarity of black hole evaporation in final-state projection models, JHEP 08, 126, 2014, [arXiv:1308.4209 [hep-th]]

    arXiv 2014

Show all 35 references
  1. [9]

    J. H. W.H. Zurek, M. Gell-Mann, Complexity, entropy and the physics of information, 1990

    1990

  2. [10]

    H. F. Dowker and J. J. Halliwell, The Quantum mechanics of history: The Decoherence functional in quantum mechanics, Phys. Rev. D 46, 1580–1609, 1992

    1992

  3. [11]

    Gell-Mann and J

    M. Gell-Mann and J. B. Hartle, Classical equations for quantum systems, Phys. Rev. D 47, 3345–3382, 1993, [arXiv:gr-qc/9210010]

    1993 arXiv

  4. [12]

    Penington, Entanglement Wedge Reconstruction and the Information Paradox, JHEP 09, 002, 2020, [arXiv:1905.08255 [hep-th]]

    G. Penington, Entanglement Wedge Reconstruction and the Information Paradox, JHEP 09, 002, 2020, [arXiv:1905.08255 [hep-th]]. 7

    2020 arXiv

  5. [13]

    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, 063, 2019, [arXiv:1905.08762 [hep-th]]

    2019 arXiv

  6. [14]

    Penington, S

    G. Penington, S. H. Shenker, D. Stanford and Z. Yang, Replica wormholes and the black hole interior, JHEP 03, 205, 2022, [arXiv:1911.11977 [hep-th]]

    2022 arXiv

  7. [15]

    Almheiri, T

    A. Almheiri, T. Hartman, J. Maldacena, E. Shaghoulian and A. Tajdini, Replica Wormholes and the Entropy of Hawking Radiation, JHEP 05, 013, 2020, [arXiv:1911.12333 [hep-th]]

    2020 arXiv

  8. [16]

    Almheiri, R

    A. Almheiri, R. Mahajan, J. Maldacena and Y. Zhao, The Page curve of Hawking radiation from semiclassical geometry, JHEP 03, 149, 2020, [arXiv:1908.10996 [hep-th]]

    2020 arXiv

  9. [17]

    Almheiri, R

    A. Almheiri, R. Mahajan and J. E. Santos, Entanglement islands in higher dimensions, SciPost Phys. 9, 001, 2020, [arXiv:1911.09666 [hep-th]]

    2020 arXiv

  10. [18]

    Almheiri, R

    A. Almheiri, R. Mahajan and J. Maldacena, Islands outside the horizon, 2019, [arXiv:1910.11077 [hep-th]]

    2019 arXiv

  11. [19]

    Almheiri, T

    A. Almheiri, T. Hartman, J. Maldacena, E. Shaghoulian and A. Tajdini, The entropy of Hawking radiation, Rev. Mod. Phys. 93, 035002, 2021, [arXiv:2006.06872 [hep-th]]

    2021 arXiv

  12. [20]

    Verlinde and H

    E. Verlinde and H. Verlinde, Black Hole Entanglement and Quantum Error Correction, JHEP 10, 107, 2013, [arXiv:1211.6913 [hep-th]]

    2013 arXiv

  13. [21]

    Papadodimas and S

    K. Papadodimas and S. Raju, An Infalling Observer in AdS/CFT, JHEP 10, 212, 2013, [arXiv:1211.6767 [hep-th]]

    2013 arXiv

  14. [22]

    Maldacena and L

    J. Maldacena and L. Susskind, Cool horizons for entangled black holes, Fortsch. Phys. 61, 781–811, 2013, [arXiv:1306.0533 [hep-th]]

    2013 arXiv

  15. [23]

    Lloyd, Almost certain escape from black holes, Phys

    S. Lloyd, Almost certain escape from black holes, Phys. Rev. Lett. 96, 061302, 2006, [arXiv:quant-ph/0406205]

    2006 arXiv

  16. [24]

    Akers, N

    C. Akers, N. Engelhardt, D. Harlow, G. Penington and S. Vardhan, The black hole interior from non-isometric codes and complexity, JHEP 06, 155, 2024, [arXiv:2207.06536 [hep-th]]

    2024 arXiv

  17. [25]

    Discussion: Some Open Questions in Quantum Gravity (2020)

    D. Stanford, “Discussion: Some Open Questions in Quantum Gravity (2020).”

    2020

  18. [26]

    Almheiri, X

    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]]

    2015 arXiv

  19. [27]

    D. L. Jafferis, A. Lewkowycz, J. Maldacena and S. J. Suh, Relative entropy equals bulk relative entropy, JHEP 06, 004, 2016, [arXiv:1512.06431 [hep-th]]

    2016 arXiv

  20. [28]

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

    2016 arXiv

  21. [29]

    Petz, Sufficient subalgebras and the relative entropy of states of a von Neumann algebra, Commun

    D. Petz, Sufficient subalgebras and the relative entropy of states of a von Neumann algebra, Commun. Math. Phys. 105, 123–131, 1986

    1986

  22. [30]

    Harlow and P

    D. Harlow and P. Hayden, Quantum Computation vs. Firewalls, JHEP 06, 085, 2013, [arXiv:1301.4504 [hep-th]]

    2013 arXiv

  23. [31]

    Oppenheim and W

    J. Oppenheim and W. G. Unruh, Firewalls and flat mirrors: An alternative to the AMPS experiment which evades the Harlow-Hayden obstacle, JHEP 03, 120, 2014, [arXiv:1401.1523 [hep-th]]

    2014 arXiv

  24. [32]

    Almheiri, D

    A. Almheiri, D. Marolf, J. Polchinski, D. Stanford and J. Sully, An Apologia for Firewalls, JHEP 09, 018, 2013, [arXiv:1304.6483 [hep-th]]

    2013 arXiv

  25. [33]

    Ali Ahmad, A

    S. Ali Ahmad, A. Almheiri and S. Lin, T T and the black hole interior, 2025, [arXiv:2503.19854 [hep-th]]

    2025 arXiv

  26. [34]

    F. A. Smirnov and A. B. Zamolodchikov, On space of integrable quantum field theories, Nucl. Phys. B 915, 363–383, 2017, [arXiv:1608.05499 [hep-th]]

    2017 arXiv

  27. [35]

    Cavagli` a, S

    A. Cavagli` a, S. Negro, I. M. Sz´ ecs´ enyi and R. Tateo, T ¯T -deformed 2D Quantum Field Theories, JHEP 10, 112, 2016, [arXiv:1608.05534 [hep-th]]

    2016 arXiv

Pith tools

Reviewed August 7, 2026 · model on record in the stance chip above.