  Heisenberg's uncertainty principle, which imposes intrinsic restrictions on
our ability to predict the outcomes of incompatible quantum measurements to
arbitrary precision, demonstrates one of the key differences between classical
and quantum mechanics. The physical systems considered in the uncertainty
principle are static in nature and described mathematically with a quantum
state in a Hilbert space. However, many physical systems are dynamic in nature
and described with the formalism of a quantum channel. In this paper, we show
that the uncertainty principle can be reformulated to include
process-measurements that are performed on quantum channels. Since both quantum
states and quantum measurements are themselves special cases of quantum
channels, our formalism encapsulates the uncertainty principle in its utmost
generality. More specifically, we obtain expressions that generalize the
Maassen-Uffink uncertainty relation and the universal uncertainty relations
from quantum states to quantum channels.
