Statement
Problem 2.3 of Goto et al.: can we reformulate QFT correlators in terms of information-theoretic tasks? The paper notes that task feasibility is bounded by entropic quantities — e.g. the optimal type-II error exponent in hypothesis testing is the relative entropy (quantum Stein’s lemma), and mutual information bounds how much local randomness a region can share.
Why It Matters
The quantum Stein’s lemma reading is a direct operational handle on the group’s central quantity: Araki–Uhlmann relative entropy is the optimal asymptotic distinguishability rate between two states. Casting the group’s closed-form relative-entropy results (coherent/squeezed/cat states vs. vacuum) as state-discrimination tasks would give them an operational meaning and feed relative-entropy-embezzlement-as-infinite-dim-qi.
What We Know
- Quantum Stein’s lemma: relative entropy = optimal type-II error exponent in asymmetric hypothesis testing (finite dim; the infinite-dim/type III₁ version is exactly the quantum-information-in-infinite-dimensions frontier).
- The group has explicit Araki–Uhlmann values for many state pairs; their operational (discrimination-rate) interpretation is available but not yet emphasized.
- Correlators ↔ mutual information ↔ shared randomness is standard in QI but under-exploited in the QFT program.
Possible Approaches
- Restate the 2025 relative-entropy results as vacuum-vs-excited discrimination-rate statements; check the infinite-dimensional Stein’s-lemma caveats.
- Bound specific smeared correlators by mutual information between regions.