  The asymptotic theory of quantum channel estimation has been well
established, but in general noiseless and controllable ancilla is required for
attaining the ultimate limit in the asymptotic regime. Little is known about
the metrological performance without noiseless ancilla, which is more relevant
in practical circumstances. In this work, we present a novel theoretical
framework to address this problem, bridging quantum metrology and the
asymptotic theory of quantum channels. Leveraging this framework, we prove
sufficient conditions for achieving the Heisenberg limit with repeated
application of the channel to estimate, both with and without applying
interleaved unitary control operations. For the latter case, we design an
algorithm to identify the control operation. Finally, we analyze several
intriguing examples by our approach.
