Quantum limits to resolution and discrimination of spontaneous emission lifetimes

In this paper 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 analog 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 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 optomolecular metrology that do not rely on multiphoton interference but evidently do benefit from a more thorough exploitation of the coherence properties of single photons.