  Physical processes in the quantum regime possess non-classical properties of
quantum mechanics. However, methods for quantitatively identifying such
processes are still lacking. Accordingly, in this study, we develop a framework
for characterizing and quantifying the ability of processes to cause
quantum-mechanical effects on physical systems. We start by introducing a new
concept, referred to as quantum process capability, to evaluate the effects of
an experimental process upon a prescribed quantum specification. Various
methods are then introduced for measuring such a capability. It is shown that
the methods are adapted to quantum process tomography for implementation of
process capability measure and applicable to all physical processes that can be
described using the general theory of quantum operations. The utility of the
proposed framework is demonstrated through several examples, including
processes of entanglement, coherence, and superposition. The formalism proposed
in this study provides a generic approach for the identification of dynamical
processes in quantum mechanics and facilitates the general classification of
quantum-information processing.
