Statement
Problem 2.6 of Goto et al.: given physically motivated operation classes in QFT (causal, compact-support, thermal, energy-bounded, symmetry-covariant), what are the associated monotones and the complete (necessary-and-sufficient) constraints governing state transformations?
Why It Matters
Araki–Uhlmann relative entropy is the prototype QFT monotone (monotone under the relevant CP maps by data processing), and the group computes it in closed form. Casting the group’s results as monotones under an explicit free class — and hunting for new monotones adapted to causal/energy-bounded operations — is a direct extension of the relative-entropy program and complements free-states-and-operations-for-resource-theory-in-qft.
What We Know
- Relative entropy is monotone under CPTP/quantum channels; the group’s data are all instances.
- Energy-bounded and thermal-operation resource theories have finite-dim monotone families; QFT analogs are largely open.
- Complete sets of constraints (à la Nielsen’s theorem for LOCC) are unknown in the type III₁ setting.
Possible Approaches
- Prove monotonicity of the group’s computed quantities under a fixed causal free class.
- Search for a second, independent monotone (beyond relative entropy) sensitive to region size / mass gap.