In this work we investigate phase estimation of a two-qubit system under the action of the quantum cyclic $n$-switch in generalized amplitude-damping, depolarizing, and phase-damping channels. Our results show that the quantum cyclic $n$-switch can improve the precision of phase estimation in correlated generalized amplitude-damping channels and uncorrelated depolarizing channels. Increasing the dimension of the control system can significantly enhance the precision. For correlated generalized amplitude-damping channels under the quantum cyclic $n$-switch, both the environmental thermal noise and the classical correlation between channels can play a positive role in improving the estimation precision. In uncorrelated depolarizing channels, the quantum cyclic $n$-switch operation could suppress the decoherence, thereby enhancing the precision of phase estimation. In correlated phase-damping channels under the action of the quantum cyclic $n$-switch, the classical correlation can eliminate the negative effect of dephasing noise on coherence to improve phase estimation.

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• Open quantum systems & decoherence
• Quantum parameter estimation