  Quantum steering is an important correlation in quantum information theory. A
recent work [Nat. Commun. 12, 2410 (2021)] showed that quantum steering is also
useful for quantum metrology. Here, we extend the exploration of
steering-enhanced quantum metrology from single noiseless phase shifts to
superpositions of noisy phase shifts. As concrete examples, we consider a
control system that manipulates a target system to pass through a superposition
of either dephased or depolarized phase shifts channels. We show that using
such superpositions of noisy phase shifts can suppress the effects of noise and
improve metrology. Furthermore, we also implemented proof-of-principle
experiments for a superposition of dephased phase shifts on the IBM Quantum
Experience, demonstrating a clear improvement on metrology.
