  We introduce a task that we call partial decoupling, in which a bipartite
quantum state is transformed by a unitary operation on one of the two
subsystems and then is subject to the action of a quantum channel. We assume
that the subsystem is decomposed into a direct-sum-product form, which often
appears in the context of quantum information theory. The unitary is chosen at
random from the set of unitaries having a simple form under the decomposition.
The goal of the task is to make the final state, for typical choices of the
unitary, close to the averaged final state over the unitaries. We consider a
one-shot scenario, and derive upper and lower bounds on the average distance
between the two states. The bounds are represented simply in terms of smooth
conditional entropies of quantum states involving the initial state, the
channel and the decomposition. Thereby we provide generalizations of the
one-shot decoupling theorem. The obtained result would lead to further
development of the decoupling approaches in quantum information theory and
fundamental physics.
