Statement
A group-specific spin-off of Problem 5.1 of Goto et al. (quantum-information-in-infinite-dimensions): can the group’s existing body of results — finite Araki–Uhlmann relative entropy for coherent, squeezed, and cat states, and the type III₁ embezzlement rate/capacity work — be assembled and framed as a concrete contribution to the “quantum information theory in infinite-dimensional Hilbert spaces” the paper calls for?
Why It Matters
Low technical risk, high visibility. The group has already computed the finite information-theoretic quantities that survive on type III₁ algebras — exactly the objects Problem 5.1 says are missing a canonical theory. A perspective/letter that positions the 2025 relative-entropy papers and the embezzlement-capacity manuscript against §5 of Goto et al. would stake a claim on a frontier a large holography/QI collaboration has just publicly prioritized.
What We Know
- Closed-form relative entropy controlled by the smeared Pauli–Jordan distribution (coherent states); distinct mass/region scaling for squeezed and two-coherent states; non-trivial dimension dependence (arXiv:2511.20244).
- Embezzlement on type III₁ is universal and arbitrarily accurate rather than exact; the group’s capacity question sharpens its cost to .
- These are precisely “finite QI quantities on infinite-dimensional algebras” — the content §5 asks to systematize.
Possible Approaches
- Draft a short position note mapping each existing result to a piece of the §5 program (which finite quantities are canonical; which need one-shot/smooth-entropy tooling; where the type II crossed product supplies a trace).
- Identify the gaps the group’s toolkit does not yet cover (interacting theories — see relative-entropy-interacting-theories; a general infinite-dim data-processing / resource framework).