  Receiver operating characteristics (ROCs) are a well-established
representation of the tradeoff between detection and false alarm probabilities
in classical binary hypothesis testing. We use classical ROCs as motivation for
two types of operating characteristics for binary hypothesis testing in quantum
systems -- decision operating characteristics (QDOCs) and measurement operating
characteristics (QMOCs). Both are described in the context of a framework we
propose that encompasses the typical formulations of binary hypothesis testing
in both the classical and quantum scenarios. We interpret Helstrom's well-known
result regarding discrimination between two quantum density operators with
minimum probability of error in this framework. We also present a
generalization of previous results regarding the correspondence between
classical Parseval frames and quantum measurements. The derivation naturally
leads to a constructive procedure for generating many different measurements
besides Helstrom's optimal measurement, some standard and others non-standard,
that achieve minimum probability of error.
