  In this work we investigate the quantum information theoretical limits to
several tasks related to lifetime estimation and discrimination of a two-level
spontaneous optical emitter. We focus in particular on the model problem of
resolving two mutually incoherent exponential decays with highly overlapping
temporal probability profiles. Mirroring recent work on quantum-inspired
super-resolution of point emitters, we find that direct lifetime measurement
suffers from an analogue of "Rayleigh's Curse" when the time constants of the
two decay channels approach one another. We propose alternative measurement
schemes that circumvent this limit, and also demonstrate superiority to direct
measurement for a related binary hypothesis test. Our findings add to a growing
list of examples in which a quantum analysis uncovers significant information
gains for certain tasks in opto-molecular metrology that do not rely on
multiphoton interference, but evidently do benefit from a more thorough
exploitation of the coherence properties of single photons.
