  We demonstrate that the negative volume of any $s$-paramatrized
quasiprobability, including the Glauber-Sudashan $P$-function, can be
consistently defined and forms a continuous hierarchy of nonclassicality
measures that are linear optical monotones. These measures therefore belong to
an operational resource theory of nonclassicality based on linear optical
operations. The negativity of the Glauber-Sudashan $P$-function in particular
can be shown to have an operational interpretation as the robustness of
nonclassicality. We then introduce an approximate linear optical monotone, and
show that this nonclassicality quantifier is computable and is able to identify
the nonclassicality of nearly all nonclassical states.
