  The time-frequency degree of freedom of the electromagnetic field is the
final frontier for single-photon measurements. The temporal and spectral
distribution a measurement retrodicts (that is, the state it projects onto) is
determined by the detector's intrinsic resonance structure. In this paper, we
construct ideal and more realistic positive operator-valued measures (POVMs)
that project onto arbitrary single-photon wavepackets with high efficiency and
low noise. We discuss applications to super-resolved measurements and quantum
communication. In doing so we will give a fully quantum description of the
entire photo detection process, give prescriptions for (in principle)
performing single-shot Heisenberg-limited time-frequency measurements of single
photons, and discuss fundamental limits and trade-offs inherent to
single-photon detection.
