  A photodetector may be characterized by various figures of merit such as
response time, bandwidth, dark count rate, efficiency, wavelength resolution,
and photon-number resolution. On the other hand, quantum theory says that any
measurement device is fully described by its POVM, which stands for
Positive-Operator-Valued Measure, and which generalizes the textbook notion of
the eigenstates of the appropriate hermitian operator (the "observable") as
measurement outcomes. Here we show how to define a multitude of photodetector
figures of merit in terms of a given POVM. We distinguish classical and quantum
figures of merit and issue a conjecture regarding trade-off relations between
them. We discuss the relationship between POVM elements and photodetector
clicks, and how models of photodetectors may be tested by measuring either POVM
elements or figures of merit. Finally, the POVM is advertised as a
platform-independent way of comparing different types of photodetectors, since
any such POVM refers to the Hilbert space of the incoming light, and not to any
Hilbert space internal to the detector.
