  We generalize the theory of catalytic quantum randomness to delocalized and
dynamical settings. First, we expand the resource theory of randomness (RTR) by
calculating the amount of entropy catalytically extractable from a correlated
or dynamical randomness source. In doing so, we show that no entropy can be
catalytically extracted when one cannot implement local projective measurement
on randomness source without altering its state. The RTR, as an archetype of
the `concave' resource theory, is complementary to the convex resource theories
in which the amount of randomness required to erase the resource is a resource
measure. As an application, we prove that quantum operation cannot be hidden in
correlation between two parties without using randomness, which is the
dynamical generalization of the no-hiding theorem. Second, we study the
physical properties of information flow. Popularized quotes like "information
is physical" or "it from bit" suggest the matter-like picture of information
that can travel with the definite direction while leaving detectable traces on
its region of departure. To examine the validity of this picture, we focus on
that catalysis of randomness models directional flow of information with the
distinguished source and recipient. We show that classical information can
always spread from its source without altering its source or its surrounding
context, like an immaterial entity, while quantum information cannot. We
suggest an approach to formal definition of semantic quantum information and
claim that utilizing semantic information is equivalent to using a partially
depleted information source. By doing so, we unify the utilization of semantic
and non-semantic quantum information and conclude that one can always extract
more information from an incompletely depleted classical randomness source, but
it is not possible for quantum randomness sources.
