  The question of how quantities, like entanglement and coherence, depend on
the number of copies of a given state $\rho$ is addressed. This is a hard
problem, often involving optimizations over Hilbert spaces of large dimensions.
Here, we propose a way to circumvent the direct evaluation of such quantities,
provided that the employed measures satisfy a self-similarity property. We say
that a quantity ${\cal E}(\rho^{\otimes N})$ is {\it scalable} if it can be
described as a function of the variables $\{{\cal E}(\rho^{\otimes
i_1}),\dots,{\cal E}(\rho^{\otimes i_q}); N\}$ for $N>i_j$, while, preserving
the tensor-product structure. If analyticity is assumed, recursive relations
can be derived for the Maclaurin series of ${\cal E}(\rho^{\otimes N})$, which
enable us to determine its possible functional forms (in terms of the mentioned
variables). In particular, we find that if ${\cal E}(\rho^{\otimes 2^n})$
depends only on ${\cal E}(\rho)$, ${\cal E}(\rho^{\otimes 2})$, and $n$, then
it is completely determined by Fibonacci polynomials, to leading order. We show
that the one-shot distillable (OSD) entanglement is well described as a
scalable measure for several families of states. For a particular two-qutrit
state $\varrho$, we determine the OSD entanglement for $\varrho^{\otimes 96}$
from smaller tensorings, with an accuracy of $97 \%$ and no extra computational
effort. Finally, we show that superactivation of non-additivity may occur in
this context.
