  We develop a framework for learning properties of quantum states beyond the
assumption of independent and identically distributed (i.i.d.) input states. We
prove that, given any learning problem (under reasonable assumptions), an
algorithm designed for i.i.d. input states can be adapted to handle input
states of any nature, albeit at the expense of a polynomial increase in copy
complexity. Furthermore, we establish that algorithms which perform
non-adaptive incoherent measurements can be extended to encompass non-i.i.d.
input states while maintaining comparable error probabilities. This allows us,
among others applications, to generalize the classical shadows of Huang, Kueng,
and Preskill to the non-i.i.d. setting at the cost of a small loss in
efficiency. Additionally, we can efficiently verify any pure state using
Clifford measurements, in a way that is independent of the ideal state. Our
main techniques are based on de Finetti-style theorems supported by tools from
information theory. In particular, we prove a new randomized local de Finetti
theorem that can be of independent interest.
