  The fidelity function of quantum states have been widely used in quantum
information science and frequently arises in the quantification of optimal
performances for the estimation and distinguish of quantum states. A fidelity
function on quantum channel is expected to have same wide applications in
quantum information science. In this paper we propose a fidelity function on
quantum channels and show that various distance measures on quantum channels
can be obtained from this fidelity function, for example the Bures angle and
the Bures distance can be extended to quantum channels via this fidelity
function. We then show that the distances between quantum channels lead
naturally to a new Fisher information which quantifies the ultimate precision
limit in quantum metrology, the ultimate precision limit can thus be seen as a
manifestation of the distances between quantum channels. We also show that the
fidelity on quantum channels provides a unified framework for perfect quantum
channel discrimination and quantum metrology, in particular we show that the
minimum number of uses needed for perfect channel discrimination is exactly the
counterpart of the precision limit in quantum metrology, and various useful
lower bounds for the minimum number of uses needed for perfect channel
discrimination can be obtained via this connection.
