The gravity/QI open-problems agenda (Goto et al.) and the group's toolkit

The Link

Goto et al. (arXiv:2606.30853) is a curated open-problems agenda from the holography/QI community, organized into four themes: operational characterization of observables, the role of observers, quantum error correction, and the infinite-dimensionality of Hilbert spaces. Read against the group’s programs, it is a second, independent open-problems list — a holography-side sibling of the IQOQI triage that produced long-range-bell-decay-project, bell-in-type-iii-project, and embezzlement-capacity-project.

The striking fact is the overlap. Two of the four themes are exactly where the group’s flat-space, type III₁, modular-theory toolkit already operates:

• Theme 4 (infinite-dimensional Hilbert spaces / type II–III algebras) is the algebraic home of the group’s Araki–Uhlmann relative entropy, embezzlement, and crossed-product work.
• Theme 1 (operational characterization / resource theory in holography) is the thesis of the group’s generalized-entropy-as-capacity result.

The other two themes (observers, QEC) are where the group is a well-positioned consumer rather than a producer.

Evidence

• Finite information on type III₁ is already built. The group’s 2025 papers compute Araki–Uhlmann relative entropy for coherent, squeezed, and cat states — finite quantities on algebras where von Neumann entropy is UV-divergent. That is a concrete instance of the “QI in infinite dimensions” the paper’s §5 asks for, not a promissory note.
• Embezzlement is native to III₁. The group studies embezzlement in type III₁ and the capacity question; van Luijk–Stottmeister–Werner–Wilming (2024) established embezzlement in QFT. This is Theme 4 machinery in hand.
• Operational characterization, made into a theorem. The holographic-embezzlement manuscript proves a bound $1-F_d\lesssim \log d/S_{\text{gen}}$ and conjectures a matching lower bound that would make generalized entropy the operational capacity — a literal answer to Theme 1’s “characterize holographic observables by the tasks they enable.”
• Tsirelson is the III₁ Bell obstruction. Theme 4 names the Tsirelson problem (tensor vs. commuting-operator correlations, ${\mathrm{MIP}}^{\ast }=\mathrm{RE}$). Wedge algebras commute but do not tensor-factorize — exactly the commuting-operator setting — which is the algebraic crux of bell-in-type-iii-project and the ceiling on vacuum Bell-CHSH.
• The observer’s algebra is course material. Theme 2’s dynamical, type-II observer is CLPW/CPW (crossed product), taught in AQFT Semester II (syllabus).

Gaps

• The group’s results are free / generalized-free field; the paper’s are holographic. The honest bridge is to present the free-field type III₁ computations as models of the infinite-dimensional QI the paper wants, flagging what is genuinely holographic input (as the wormholes thread already does).
• Capacity, not yet proved. The generalized-entropy-as-capacity claim is a bound until the lower bound is closed; Theme 1’s “operational characterization” is only fully answered when it is.
• Themes 2–3 need bulk input the flat-space toolkit does not supply. Observer backreaction and non-isometric codes are bulk/holographic statements; the group can consume but not (yet) derive them.
• Tsirelson link is structural, not yet computed. That wedge algebras are commuting-operator is clear; whether the commuting-operator vs. tensor distinction changes any number the group computes (e.g. the achievable CHSH value or its $L$-decay) is open.

Potential Projects

• P1 — Position note: “the group’s relative entropy + embezzlement work as QI in infinite dimensions” (most immediate). Frame the 2025 relative-entropy papers and the embezzlement-capacity manuscript explicitly against §5 of Goto et al.; a short perspective/letter staking the claim that finite Araki–Uhlmann quantities are the infinite-dimensional QI the agenda calls for. Low technical risk, high visibility.
• P2 — Tsirelson obstruction for vacuum Bell-CHSH (most fundamental). Make precise whether the commuting-operator character of wedge algebras (vs. any tensor-factorized model) constrains the achievable Bell-CHSH value or its β(L) decay. Feeds bell-in-type-iii-project directly.
• P3 — Generalized entropy as operational capacity (most distinctive). Close the lower bound so the capacity result answers Theme 1’s operational-characterization challenge with a theorem, not a slogan.
• P4 — Observer-algebra Bell-CHSH (most speculative). Redo a Bell-CHSH / relative-entropy computation on the type-II crossed-product “observer’s algebra,” giving a bounded-energy physical observer and possibly sidestepping impossible measurements. Connects Theme 2 to bell-chsh-in-holographic-setting.

Related

• 2026-goto-rethinking-qi-gravity-fields — the paper page carries the full catalogue of all 20 problem pages, grouped by theme.
• strings-2026-open-questions — the string-theory community’s parallel open-problems list (Ooguri, Strings 2026); the QI/QG subset (Dabholkar EE-in-gravity, Gesteau emergence, Chester finite-N, Takayanagi holography-as-quantum-computer) maps this agenda from the other side.
• The group-tractable spin-offs: quantum-information-in-infinite-dimensions (5.1), tsirelson-problem-vacuum-bell-chsh, relative-entropy-embezzlement-as-infinite-dim-qi, observer-algebra-bell-chsh, dynamical-observer-backreaction-and-algebra (3.4), holographic-resource-theory (2.8), qft-correlators-as-information-tasks (2.3).
• long-range-bell-decay-project, bell-in-type-iii-project, embezzlement-capacity-project
• wormholes-and-quantum-information-qft, type-iii-algebras-across-areas, holographic-bell-program, crossed-product-and-island-formula
• embezzlement-capacity-lower-bound, holographic-dual-embezzlement-protocol, bell-chsh-in-holographic-setting, long-range-bell-decay
• gauge-gravity-duality, bell-inequalities-qft, relative-entropy-qft