Work fluctuations for quantum states with energy coherence
In plain words
The usual way to measure work, measuring energy before and after, destroys superpositions between energy levels. A 2017 theorem showed no measurement scheme both keeps the standard results and gives the right average work for every state.
Precise statement
Perarnau-Llobet et al. (PRL 2017) proved that no POVM-based work distribution $P(W)$ both reproduces two-point-measurement statistics for states diagonal in energy and gives $\langle W\rangle = \operatorname{Tr}[\rho (U^{\mathrm{dag}} H_1 U - H_0)]$ for all states. Determine which relaxed object (a quasiprobability such as Kirkwood-Dirac or Margenau-Hill, or a disturbing measurement scheme) is the operationally correct description of work for coherent states, judged by fluctuation theorems and experimental accessibility.
What would settle it
Operational criteria with a proof that one definition uniquely meets them, plus an experiment measuring it.