Statement
Problem 2.5 of Goto et al.: to build a resource theory in QFT one must fix a class of free operations , but the choice is subtle — it must respect locality, causality, and sometimes spacetime symmetry. Natural candidates are operations localized in spacetime regions (i.e. maps on the von Neumann algebras of those regions), possibly with classical communication.
Why It Matters
This is resource theory phrased in exactly the group’s language: operations on local algebras, causal constraints, modular structure. The group’s embezzlement and relative-entropy work implicitly picks free operations (Weyl/Gaussian, causal); making that choice explicit is a natural way to systematize the quantum-information-in-infinite-dimensions program.
What We Know
- In finite-dim QI, LOCC / separable / PPT operations define entanglement resource theories.
- In QFT the analog must be algebra-preserving and causal; “causal operations” and “operations with compact spacetime support” are the paper’s suggested classes.
- The group already works with a de facto free class (Weyl operators, Bogoliubov/Gaussian maps).
Possible Approaches
- Fix a causal free-operation class on wedge/diamond algebras and identify the induced resource (entanglement? coherence? athermality?).
- Tie the free class to the split property (which supplies an intermediate type-I factor and a tensor structure).