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REVIEW 3 major objections 5 minor 8 cited by

Emergent Holographic Spacetime from Quantum Information

T0 review · 3 major / 5 minor · reviewed 2026-08-07 · deepseek-v4-flash

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Pith's one-line read The paper claims that gravitational spacetime is built from entangled qubits and that the imaginary part of pseudo-entropy is the seed of emergent time.

desk verdict A well-crafted roadmap of the quantum-information view of holography, honest about open problems; the emergent-time proposal is a speculation, not a demonstrated result, and its pseudo-entropy mechanism needs a branch prescription. read the letter →

arxiv 2506.06595 v2 pith:KE6DBYPW submitted 2025-06-07 hep-th cond-mat.str-elgr-qcquant-ph

Tadashi Takayanagi This is my paper
classification hep-thcond-mat.str-elgr-qcquant-ph
keywords holographicdualityAdS/CFTentanglemententropypseudo-entropyemergentspacetimetimedeSitterholographyquantumgravity
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

This essay argues that AdS/CFT, read through quantum information, says spacetime is not fundamental: it is an emergent description of an enormous number of entangled qubits. On this picture, the extra spatial coordinate of anti-de Sitter space arises from entanglement, and gravitational waves are dynamical evolutions of quantum entanglement. The central open problem it addresses is time, and the author proposes that the imaginary part of pseudo-entropy, a complex-valued generalization of entanglement entropy, is the quantity from which the time coordinate of holographic spacetimes emerges, especially in de Sitter holography. The essay lays out a research program: identify the quantum circuits dual to concrete string-theory examples, extend holography to cosmological spacetimes, and treat gravity as the dynamics of a quantum computer. A sympathetic reader cares because this points toward a formulation of quantum gravity in which the creation of the Universe is described by ordinary quantum information processing.

What carries the argument

The central object is the holographic entanglement entropy formula $S_A = \mathrm{Ext}_{\Gamma_A} A(\Gamma_A)/(4G_N)$, generalized to pseudo-entropy by replacing the reduced density matrix $\rho_A$ with the reduced transition matrix $\tau_A = \mathrm{Tr}_{\bar A} |\Psi_i\rangle\langle\Psi_f| / \langle\Psi_f|\Psi_i\rangle$. Because $\tau_A$ is non-Hermitian, pseudo-entropy can take complex values, and the imaginary part is tied to time-like extremal surfaces and non-Hermitian density matrices; the essay proposes this imaginary part as the mechanism of emergent time. Supporting machinery includes tensor networks and quantum circuits as toy models of holography, the island formula and replica wormholes for the Page curve, and the interpretation of AdS/CFT as a quantum computer.

What would settle it

A quantum simulator measurement of pseudo-entropy in a candidate holographic lattice model that yields a vanishing imaginary part while the dual geometry has time-like geodesics would undercut the emergent-time mechanism; so would a rigorous no-go result ruling out a consistent, unitary dS/CFT correspondence.

Watch

Extended reading notes

Core claim

The core claim is that the holographic entanglement entropy formula, which computes entanglement entropy from the area of an extremal surface, implies that every Planck-scale area of spacetime carries a Bell pair of qubits, so that spacetime is a collection of entangled qubits. The essay's new proposal is that the imaginary part of pseudo-entropy, defined from the reduced transition matrix between two different states, gives the emergent time coordinate, while its real part gives the emergent space coordinate. In dS3/CFT2 the dual CFT is non-unitary with an imaginary central charge, and the geodesic length that computes pseudo-entropy becomes complex because part of the geodesic is time-like; the imaginary part is proportional to the imaginary central charge. Thus time emerges from the non-Hermiticity of the density matrix and is naturally absent in unitary AdS/CFT setups.

Load-bearing premise

The whole argument presupposes that holographic duality is correct for the spacetimes considered, and the essay itself concedes that there is no complete proof of AdS/CFT, with dS/CFT being even more conjectural.

Editorial extensions

If this is right

  • If time emerges from imaginary pseudo-entropy, holographic duals of cosmological spacetimes must be non-unitary, and the imaginary central charge in dS3/CFT2 is a concrete signature of that non-unitarity.
  • The island formula's derivation of the Page curve implies that information is not lost during black hole evaporation, resolving the black hole information paradox.
  • Identifying the quantum circuits dual to known AdS/CFT examples would let us read off bulk geometry from circuit structure and could guide the design of new quantum computers.
  • Gravity edge modes suggest that gravitons are bound states of more fundamental degrees of freedom and that dividing spacetime along a surface deconfines gravity, explaining the O(N^2) entropy of black holes.
  • Extending holography to spacetimes like de Sitter space would let quantum information tools probe the origin of the Universe without needing a complete microscopic theory of quantum gravity.

Reading between the lines

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

  • If the pseudo-entropy proposal is right, a quantum simulator that measures pseudo-entropy, for instance through postselected or weak-measurement protocols, could test the emergent-time mechanism in tabletop experiments without needing a real de Sitter space.
  • The author's emphasis on non-unitarity suggests a sharp criterion: holographic duals with real, positive central charge should not exhibit emergent time, so time emergence is tied directly to complex CFT data.
  • One could extend the proposal by defining a circuit complexity for the time direction, connecting the imaginary part of pseudo-entropy to the number of non-unitary gates in Euclidean path-integral optimization.
  • The gravity-edge-mode analogy predicts a boundary contribution to entanglement that scales with area when a gravitational system is divided; quantum Hall simulators that probe both boundary and bulk physics might be a place to look for this signature.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 5 minor

Summary. This Essay argues that holographic duality, specifically AdS/CFT and its conjectural dS/CFT extension, indicates that gravitational spacetime and even time itself may emerge from quantum entanglement in a boundary many-body system. It reviews the Ryu-Takayanagi formula, quantum extremal surfaces, the island formula, entanglement wedge reconstruction, tensor network models, quantum computational complexity, and the black hole information problem. The central new proposal is that the imaginary part of pseudo-entropy, defined in Eq. (6), provides a mechanism for emergent time, especially in dS3/CFT2 where the dual central charge becomes imaginary. The Essay is presented as a vision statement rather than as a derivation, and it repeatedly acknowledges open problems.

Significance. If the proposed picture is correct, it would be a significant step toward deriving gravitational spacetime and time from quantum information. The Essay is useful as a concise roadmap and is honest about many limitations: it explicitly states that there is no complete proof of AdS/CFT, that a precise tensor network description of genuine gravitational spacetime is lacking, and that the quantum-information interpretation of the imaginary part of pseudo-entropy is an open problem. It connects a wide range of published results, including the Ryu-Takayanagi formula, the island formula, path-integral optimization, and recent dS/CFT computations, with appropriate references. The main weaknesses are that the pivotal pseudo-entropy mechanism is under-specified because of the branch ambiguity of the matrix logarithm, and the abstract overstates the epistemic status of the emergence claim relative to the body of the Essay.

major comments (3)
  1. [Pseudo-entropy and emergent time, Eq. (6)] The central mechanism is not well-defined as stated. Because τ_A = Tr_{\bar A} |Ψ_i⟩⟨Ψ_f|/⟨Ψ_f|Ψ_i⟩ is non-Hermitian, the matrix logarithm log τ_A is multi-valued when τ_A has complex eigenvalues, and the imaginary part of S_p^{(A)} depends on the branch chosen for each eigenvalue. The Essay does not specify a branch prescription, such as a principal branch, analytic continuation from Rényi entropies, or continuity in a parameter. Since the claim that time emerges from the imaginary part of pseudo-entropy, and the identification with the imaginary central charge in dS3/CFT2, rely on this quantity, the proposal needs a precise branch prescription and a demonstration that the emergent-time observable is branch-independent. The text notes that the quantum-information interpretation is an open problem, but this is a more basic definitional issue that must be addressed first.
  2. [Abstract and introduction] The abstract's statement 'This implies that a gravitational spacetime can emerge from an enormous number of entangled qubits' is stronger than what the body establishes. In the section 'From black hole to holography', the author states 'we do not have any complete proof of the AdS/CFT correspondence', and in 'Emergent spacetime from entanglement' the author writes 'we still lack a precise understanding of how a genuine gravitational spacetime is described by a tensor network'. The body appropriately uses 'suggests' and 'may', so the abstract should match this hedged epistemic status. This matters because the load-bearing conclusion of the Essay is the emergence claim, and overstating it misrepresents the evidence presented.
  3. [Pseudo-entropy and emergent time, dS3/CFT2 discussion] The application to dS3/CFT2 assumes the validity of dS/CFT and the Hartle-Hawking state, and the Essay itself acknowledges that dS/CFT is considerably more challenging than AdS/CFT and that the dual CFT is non-unitary. This is not by itself a defect, but the reader should be told whether the emergent-time proposal is a concrete prediction that can fail or a heuristic analogy. A specific test, such as computing the branch-defined imaginary part of pseudo-entropy in a concrete CFT and comparing it with the bulk geodesic length, would strengthen the claim and clarify its falsifiability.
minor comments (5)
  1. [From black hole to holography] In the paragraph on dS/CFT, 'Hartle-Gravity state' appears to be a typo for 'Hartle-Hawking state'.
  2. [Holographic entanglement and beyond] The phrase 'gravity edge modes . [21–23]' has a stray period before the citation; it should be 'gravity edge modes [21–23].'
  3. [Gravity as a quantum computer] The sentence 'the so-called local Hamiltonian problem , is known to be QMA-complete' contains an ungrammatical comma and would read better as 'the so-called local Hamiltonian problem is known to be QMA-complete'.
  4. [Holographic entanglement and beyond, Eq. (2)] The notation Ext_{\Gamma_A} is introduced without a brief definition; for a reader outside the field, it would help to state explicitly that the extremum is taken over surfaces Γ_A ending on ∂A at the AdS boundary.
  5. [Pseudo-entropy and emergent time] The references [103,104] are cited for time-like entanglement measurements, but the text does not explain whether these are experimental measurements, numerical simulations, or analytic computations; a short clarification would help.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the essay's load-bearing claims rest on independently cross-checked holographic formulas, and the emergent-time proposal is explicitly heuristic rather than derived from a fitted input.

full rationale

The essay is a perspective/research-vision document, not a closed derivation, and I find no circular reduction in its argument chain. The load-bearing ingredient, holographic entanglement entropy (Eq. (2)), is anchored by independent checks: the text states that 'the direct CFT calculations [12–14] perfectly match with Eq. (2)' and cites bulk derivations [17,18]. The pseudo-entropy definition (Eqs. (5)–(6)) is explicit, and the statement that holographic pseudo-entropy is again given by the extremal-area formula is attributed to a published, parameter-free derivation [96], not to a fit within this paper. Likewise, the dS3/CFT2 discussion invokes the known imaginary central charge [105,110] and geodesic-length results [97,98,115], and the claim about emergent time is explicitly couched as a suggestion ('This suggests that the time coordinate in dS3 may emerge from the imaginary part of pseudo-entropy'), not as a consequence obtained by defining time as that imaginary part. No fitted parameter is renamed as a prediction, and no uniqueness theorem from the author's prior work is used to forbid alternatives. The paper's own caveats, including the lack of a complete proof of AdS/CFT and the statement that the quantum-information interpretation of the imaginary part of pseudo-entropy is 'an important open problem', are limitations on the proposal's certainty, but they are not circularity. Self-citations appear throughout, yet the load-bearing ones point to independently published, externally checkable results; they do not reduce the central vision to the mere restatement of its inputs.

Assumptions & free parameters 0 free parameters · 5 assumptions · 0 invented entities

No free parameters are fitted anywhere. The central content is drawn from prior literature: holographic entanglement entropy, quantum extremal surfaces, island formula, tensor networks, and pseudo-entropy are all cited to earlier papers. The essay adds a conceptual framing but no new adjustable constants and no new physical entities.

assumptions (5)
  • domain assumption AdS/CFT correspondence is a valid exact duality between d+1 dimensional quantum gravity and d dimensional CFT.
    Invoked throughout as the foundation of holographic entanglement entropy, pseudo-entropy, and tensor network models. The essay admits no complete proof exists.
  • domain assumption Holographic entanglement entropy formula SA = Ext (A(ΓA)/(4GN)) correctly computes boundary entanglement entropy.
    The essay relies on this formula as established fact, citing Ryu-Takayanagi and later derivations. Its extension to complex-valued pseudo-entropy is central to the proposed emergent-time mechanism and is not proven in the essay.
  • domain assumption Quantum extremal surface formula and island formula give the correct quantum-corrected entanglement entropy, including the Page curve for evaporating black holes.
    Used to argue that information is not lost and that gravity modifies Hilbert space structure. The essay notes the Lorentzian derivation remains incomplete.
  • domain assumption dS/CFT holds with a Euclidean CFT at future infinity and the central charge of the dual CFT is imaginary in the classical gravity limit.
    This underpins the claim that the imaginary part of pseudo-entropy encodes emergent time. The essay acknowledges dS/CFT is less established than AdS/CFT and the dual CFT is non-unitary.
  • domain assumption Gravity edge modes are the emergent degrees of freedom that account for O(N^2) black hole entropy when a gravitational region is divided.
    Proposed by analogy with topological materials and open-closed string duality; the essay admits a precise string theory calculation has not been performed.

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Cite this review

Pith. "Pith review of Emergent Holographic Spacetime from Quantum Information." pith.science (2026). https://pith.science/paper/KE6DBYPW

@misc{pith2026250606595,
  author       = {Pith},
  title        = {Pith review of: Emergent Holographic Spacetime from Quantum Information},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/KE6DBYPW}},
  note         = {Machine review of arXiv:2506.06595}
}
read the original abstract

Holographic duality describes gravitational theories in terms of quantum many-body systems. In holography, quantum information theory provides a crucial tool that directly connects microscopic structures of these systems to the geometries of gravitational spacetimes. One manifestation is that the entanglement entropy in quantum many-body systems can be calculated from the area of an extremal surface in the corresponding gravitational spacetime. This implies that a gravitational spacetime can emerge from an enormous number of entangled qubits. In this Essay, I will discuss open problems in this area of research, considering recent developments and outlining future prospects towards a complete understanding of quantum gravity. The first step in this direction is to understand what kind of quantum circuits each holographic spacetime corresponds to, drawing on recent developments in quantum complexity theories and studying concrete examples of holography in string theory. Next, we should extend the concept of holography to general spacetimes, e.g., those spacetimes which appear in realistic cosmologies, by utilizing the connections between quantum information and holography. To address the fundamental question of how time emerges, I will propose the concepts of pseudo-entropy and time-like entanglement as a useful tool in our exploration.

Figures

Figures reproduced from arXiv: 2506.06595 by the authors.

Figure 1
Figure 1. FIG. 1. Sketches of AdS/CFT and holographic entanglement [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. Sketches of dS [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗

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Forward citations

Cited by 8 Pith papers

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