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Rethinking quantum information in gravity and fields

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Summary

A position / open-problems paper by a nine-author collaboration of Japanese theorists (Goto, Hamada, Kato, Mori, Nakata, Watanabe, Yamasaki, Yamazaki, Yoda; RIKEN iTHEMS, Osaka, KEK, Nagoya, Rikkyo, Science Tokyo, YITP, U. Tokyo, Kyoto), curating research questions at the intersection of quantum gravity and quantum information. It is not a research paper reporting theorems: it is a deliberately chosen list of problems the authors regard as important for both communities, written to get the two fields talking to each other.

The discussion is organized into four themes:

  1. Operational characterization of observables (§2) — can gravitational/holographic observables (quantum extremal surfaces, dressed bulk operators, correlators) be characterized operationally, via the information-processing tasks they enable, rather than by fiat? Sub-questions connect OTOCs to channel capacity, apply resource theories to holography, formalize bulk causality as the “connected wedge theorem,” and ask where genuine quantum-gravity effects give a computational advantage.
  2. The role of observers (§3) — what reference structure is needed to define an observable in quantum gravity; are observers emergent, fundamental, or descriptive artifacts; what are the fundamental (complexity-theoretic, state-dependent) limits on an observer’s access to the bulk; and how does a dynamical observer backreact on the semiclassical geometry and on the observable algebra?
  3. Quantum error correction (§4) — refining the Hayden–Preskill toy model toward realistic black-hole physics, and asking whether full quantum-information protection is even required in quantum gravity (approximate / non-isometric codes).
  4. Infinite-dimensionality of Hilbert spaces (§5) — the call to establish quantum information theory in infinite-dimensional Hilbert spaces, i.e. for the type II and type III von Neumann algebras that actually appear in QFT and gravity, where standard finite-dimensional QI intuitions (density matrices, von Neumann entropy, Schmidt decomposition) break down.

For this wiki the paper functions as a second open-problems agenda — a holography/QI-community companion to the group’s own IQOQI Open Quantum Problems triage (the long-range-bell-decay-project / bell-in-type-iii-project / embezzlement-capacity-project roadmap). Its Theme 4 is, almost verbatim, the frontier the group’s own programs sit on: Araki–Uhlmann relative entropy as the finite information measure on type III₁ algebras, entanglement embezzlement in type III₁, and the crossed product as the type II regulator. That makes this an unusually high-value external landmark to hold in the wiki.

Key Results

(This is a position paper; the “results” below are the open problems it curates, grouped by theme. Problem numbering follows the paper’s four sections.)

Theme 1 — Operational characterization of observables (§2).

  • Whether gravitational observables (extremal surfaces, dressed bulk operators) can be characterized operationally by the boundary tasks or information-processing capabilities they support.
  • Reformulating QFT correlators as information-theoretic tasks; connecting OTOCs and scrambling to channel capacity.
  • Bulk causality as boundary information-processing — the connected wedge theorem relating bulk causal structure to preshared correlations and nonlocality on the boundary.
  • Importing resource theories (free operations, free states, monotones) into holography and QFT — e.g. RG flow / - and -theorems as monotones; “holographic LOCC.”
  • Identifying tasks where genuine quantum-gravity effects provide a computational advantage.

Theme 2 — The role of observers (§3).

  • What reference structure is required before an observable is even definable in quantum gravity.
  • Whether observers are emergent, fundamental, or descriptive artifacts.
  • Fundamental limits on an observer’s access to the bulk: complexity-theoretic obstructions (Harlow–Hayden decoding, Python’s Lunch) and state-dependent reconstruction (Papadodimas–Raju mirror operators).
  • Backreaction of a dynamical observer on semiclassical geometry and on the observable algebra — the crossed-product / CLPW “observer’s algebra” made type II by a bounded-below observer Hamiltonian.
  • Measurement theory incorporating stringy (non-local) interactions.

Theme 3 — Quantum error correction (§4).

  • Refining the Hayden–Preskill black-hole toy model toward realistic evaporation and the Page curve.
  • Whether full QI protection is required in gravity, given non-isometric bulk-to-boundary maps and only-approximate holographic codes.

Theme 4 — Infinite-dimensionality of Hilbert spaces (§5).

  • The overarching call to build a quantum information theory valid in infinite-dimensional Hilbert spaces, and specifically on the type III₁ von Neumann algebras of QFT and gravity, where von Neumann entropy is UV-divergent and reduced density matrices do not exist.
  • Operator-algebra quantum error correction (OAQECC) beyond finite dimension.
  • The Tsirelson problem (tensor-product vs. commuting-operator correlations; the resolution) as the sharp infinite-dimensional obstruction lurking behind nonlocal games and Bell correlations.

Methods

As a survey the paper draws on a wide toolkit rather than deriving one result; the frameworks it leans on are exactly the ones the group and its AQFT/AdS-CFT courses use:

  • Algebraic QFT — III von Neumann algebras, modular theory, causal diamonds, the crossed product.
  • Holography — RT / quantum extremal surfaces, the island formula, entanglement-wedge reconstruction and subregion–subalgebra duality, large-N factorization.
  • Operational QI & resource theory — LOCC, channel capacity, hypothesis testing, entanglement distillation/dilution, state merging, free-operation monotones.
  • Quantum error correction — code subspaces, holographic/operator-algebra codes, non-isometric codes.
  • Relativistic QI — Unruh–DeWitt detectors, quantum reference frames, spacetime localization.
  • Complexity theory — computational indistinguishability, pseudorandom/pseudoentangled states, Harlow–Hayden and Python’s-Lunch hardness.
  • Soluble models — JT gravity, double-scaled SYK (a gravity dual with a finite-dimensional bulk Hilbert space), celestial holography.

Relevance

This is the most direct external validation to date of the bet the group’s whole current program is placing — that the right information-theoretic quantities on type III₁ algebras are the frontier — and it maps cleanly onto the group’s OQP roadmap (long-range-bell-decay-project, bell-in-type-iii-project, embezzlement-capacity-project) and the wormholes ↔ QI thread.

  • Theme 4 is the group’s home turf. “Establish QI theory in infinite-dimensional Hilbert spaces / type II–III algebras” is precisely what the Araki–Uhlmann relative entropy line does (finite where von Neumann entropy diverges), what the embezzlement work does (embezzlement is native to type III₁), and what the crossed product does (promoting III₁ to a traceable type II). The group is already writing chapters of the very program this paper flags as open.
  • The Tsirelson problem ↔ Bell in type III₁. Theme 4’s infinite-dimensional obstruction (tensor vs. commuting-operator correlations) is exactly the distinction at issue in bell-in-type-iii-project (OQP #1/26/32, Werner/Gill/Gisin) and in whether the vacuum’s Bell-CHSH violation saturates Tsirelson on commuting wedge algebras — see also long-range-bell-decay.
  • Theme 1 ↔ embezzlement capacity. “Characterize holographic observables by the tasks they enable / import resource theory into holography” is the thesis of the group’s generalized-entropy-as-capacity manuscript and the capacity lower-bound question: generalized entropy as the operational capacity for holographic embezzlement is a concrete instance of the operational characterization this theme asks for.
  • Theme 2 ↔ crossed product / observer. The dynamical-observer, type-II “observer’s algebra” is the CLPW/CPW material of the AQFT course Semester II, and the natural setting for a physical-observer version of the group’s Bell-CHSH and relative-entropy computations — cf. bell-chsh-in-holographic-setting.
  • Theme 3 ↔ holography scaffolding. Hayden–Preskill, the Page curve, and holographic codes are covered in the holography course of gravity duality (Lecture 24 and Lecture 18); this theme is where the group’s toolkit is currently a consumer rather than a producer.
  • Meta-point. An independent, holography-side community explicitly naming “operational characterization” and “QI in infinite dimensions” as the two central frontiers is strong outside confirmation that the group’s OQP roadmap is aimed at live, high-attention targets.

Questions Raised

  1. Do the group’s finite Araki–Uhlmann relative entropy results and its type III₁ embezzlement-rate machinery already constitute publishable pieces of the “QI in infinite dimensions” program (Theme 4)? A short position note framing the 2025 relative-entropy papers + the embezzlement-capacity manuscript against §5 could stake that claim. → embezzlement-cost-relative-entropy, relative-entropy-interacting-theories
  2. Is the Tsirelson problem the sharp infinite-dimensional obstruction for vacuum Bell-CHSH in QFT — i.e. does the commuting-operator (wedge-algebra) value differ from any tensor-factorized model, and does that matter for the β(L) decay law? → bell-in-type-iii-project
  3. Can “operational characterization of holographic observables via tasks” (Theme 1) be realized concretely by proving generalized entropy is the embezzlement capacity — turning a slogan into a theorem? → embezzlement-capacity-project, embezzlement-capacity-lower-bound, holographic-dual-embezzlement-protocol
  4. Does the type-II observer’s algebra (Theme 2) give a physically-honest home for Bell-CHSH and relative-entropy computations with a bounded-energy observer, sidestepping the impossible-measurements worry? → bell-chsh-in-holographic-setting

Problem Pages

Each of the paper’s 20 formal problems (Appendix A) has its own question page, connected to the group’s programs where possible. Priority tags reflect relevance to the group’s toolkit, not the paper’s own emphasis.

Theme 1 — Operational characterization (§2)

Theme 2 — Observer (§3)

Theme 3 — Quantum error correction (§4)

Theme 4 — Infinite dimensionality (§5)

Group-specific spin-offs (the group’s own research angles on the above)

  • 2025-liu-lectures-entanglement-vna — Liu’s review; the type III₁ / crossed-product machinery this paper’s Theme 4 calls to develop.
  • 2021-kundu-wormholes-holography — Kundu’s wormhole review; the Theme 2–3 bulk (Page curve, traversability, ER=EPR) side.
  • Witten (2022), Gravity and the crossed product (arXiv:2112.12828) — the type II observer’s algebra behind Theme 2 (in Zotero, key KAQN5465).
  • Chandrasekaran, Penington, Witten (2023), Large N algebras and generalized entropy (arXiv:2209.10454) — CPW; two-sided crossed product, covered in the AQFT course.
  • Chandrasekaran, Longo, Penington, Witten (2022), An algebra of observables for de Sitter space (arXiv:2206.10780) — CLPW; the observer’s algebra as type II₁.
  • Hayden, Preskill (2007), Black holes as mirrors (arXiv:0708.4025) — the Theme 3 toy model.
  • van Luijk, Stottmeister, Werner, Wilming (2024) — embezzlement in QFT / type III₁; background for the group’s embezzlement line.

See Also

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