Cooperation between coherent controls and noises in quantum metrology*

Standard schemes in quantum parameter estimation usually assume the parameter to be estimated residing in one part of the dynamics, either in the Hamiltonian or in the noisy process. In this article, we show that the cooperation between coherent controls and noises can create multiple paths for parametrization which goes beyond the standard schemes and opens new possibilities for further improvement on the precision limit. We demonstrate the effect of the cooperative interplay between coherent controls and the noises through canonical examples in quantum metrology and show that the cooperative scheme beats the standard scheme, and in certain regimes, the precision limit under the cooperative scheme can surpass the ultimate limit under the ideal unitary dynamics.