  Genuinely quantum states of a harmonic oscillator may be distinguished from
their classical counterparts by the Glauber-Sudarshan P-representation -- a
state lacking a positive P-function is said to be nonclassical. In this paper,
we propose a general operational framework for studying nonclassicality as a
resource in networks of passive linear elements and measurements with
feed-forward. Within this setting, we define new measures of nonclassicality
based on the quantum fluctuations of quadratures, as well as the quantum Fisher
information of quadrature displacements. These lead to fundamental constraints
on the manipulation of nonclassicality, especially its concentration into
subsystems, that apply to generic multi-mode non-Gaussian states. Special cases
of our framework include no-go results in the concentration of squeezing and a
complete hierarchy of nonclassicality for single mode Gaussian states.
