  We prove that $\textit{almost all}$ quantum states, when sampled according to
the Haar measure over the unitary group, have the following property: if copies
of the state are measured to provide latent random variables which are taken as
an input in a classical generative model or sampling algorithm, then any
alternative state whose measurements can generate the same set of target
distributions will do so with the same overall cost. Here, we define the
overall cost as the aggregate computational complexity of sampling from all
possible distributions that can be prepared from the given input distribution.
Our result holds for any length of input and output bitstring and when a
uniformly random bitstring of any length is optionally provided as an
additional resource. As it is easy to construct scenarios where a pair of
alternative candidate states are such that classical simulation of the
preparation thereof is easy in one case and hard in the other, the result can
be viewed as decoupling how hard it is to obtain a latent random variable, and
how useful it is as a resource in classical sampling and generative modelling.
