  Entanglement is sometimes helpful in distinguishing between quantum
operations, as differences between quantum operations can become magnified when
their inputs are entangled with auxiliary systems. Bounds on the dimension of
the auxiliary system needed to optimally distinguish quantum operations are
known in several situations. For instance, the dimension of the auxiliary space
never needs to exceed the dimension of the input space of the operations for
optimal distinguishability, while no auxiliary system whatsoever is needed to
optimally distinguish unitary operations. Another bound, which follows from
work of R. Timoney, is that optimal distinguishability is always possible when
the dimension of the auxiliary system is twice the number of operators needed
to express the difference between the quantum operations in Kraus form. This
paper provides an alternate proof of this fact that is based on concepts and
tools that are familiar to quantum information theorists.
