  The diverse range of resources which underlie the utility of quantum states
in practical tasks motivates the development of universally applicable methods
to measure and compare resources of different types. However, many of such
approaches were hitherto limited to the finite-dimensional setting or were not
connected with operational tasks. We overcome this by introducing a general
method of quantifying resources for continuous-variable quantum systems based
on the robustness measure, applicable to a plethora of physically relevant
resources such as optical nonclassicality, entanglement, genuine
non-Gaussianity, and coherence. We demonstrate in particular that the measure
has a direct operational interpretation as the advantage enabled by a given
state in a class of channel discrimination tasks. We show that the robustness
constitutes a well-behaved, bona fide resource quantifier in any convex
resource theory, contrary to a related negativity-based measure known as the
standard robustness. Furthermore, we show the robustness to be directly
observable -- it can be computed as the expectation value of a single witness
operator -- and establish general methods for evaluating the measure.
Explicitly applying our results to the relevant resources, we demonstrate the
exact computability of the robustness for several classes of states.
