  We study optimal perfect distinguishability between a unitary and a general
quantum operation. In 2-dimensional case we provide a simple sufficient and
necessary condition for sequential perfect distinguishability and an analytical
formula of optimal query time. We extend the sequential condition to general
d-dimensional case. Meanwhile, we provide an upper bound and a lower bound for
optimal sequential query time. In the process a new iterative method is given,
the most notable innovation of which is its independence to auxiliary systems
or entanglement. Following the idea, we further obtain an upper bound and a
lower bound of (entanglement-assisted) q-maximal fidelities between a unitary
and a quantum operation. Thus by the recursion in [1] an upper bound and a
lower bound for optimal general perfect discrimination are achieved. Finally
our lower bound result can be extended to the case of arbitrary two quantum
operations.
