  Recent technical advances have sparked renewed interest in physical systems
that couple simultaneously to different parts of the electromagnetic spectrum,
thus enabling transduction of signals between vastly different frequencies at
the level of single photons. Such hybrid systems have demonstrated frequency
conversion of classical signals and have the potential of enabling quantum
state transfer, e.g., between superconducting circuits and traveling optical
signals. This article describes a simple approach for the theoretical
characterization of the performance of quantum transducers. Given that, in
practice, one cannot attain ideal one-to-one quantum conversion, we explore how
well the transducer performs in scenarios ranging from classical signal
detection to applications for quantum information processing. While the
performance of the transducer depends on the particular application in which it
enters, we show that the performance can be characterized by defining two
simple parameters: the signal transfer efficiency $\eta$ and the added noise
$N$.
