  Randomness can help one to implement quantum maps that cannot be realized in
a deterministic fashion. Recently, it was discovered that explicitly treating a
randomness source as a quantum system could double the efficiency as a catalyst
for some tasks. In this work, we first show that every quantum channel that can
be implemented with a randomness source without leaking information to it must
be a catalysis. For that purpose, we prove a new no-go theorem that generalizes
the no-hiding theorem, the no-secret theorem that states no quantum information
can be shared with other system as a secret without leaking some information.
Second, we show that non-degenerate catalysts should be used classically when
no extra dimension is allowed, which leads to the fact that the quantum
advantage of a catalytic process strictly comes from the uniformness of the
randomness source. Finally, we discuss a method to circumvent the previous
result that achieves quantum advantage with non-degenerate catalyst uniformized
by employing extra work space.
