Multi-channel quantum parameter estimation

The aim of quantum metrology is to exploit quantum effects to improve the precision of parameter estimation beyond its classical limit. In this paper, we investigate the quantum parameter estimation problem with multiple channels. It is related but not limited to the following two important and practical quantum metrology problems:(i) Quantum enhanced metrology with control, whose aim is to improve the precision of quantum sensing by utilizing feedback or open-loop control;(ii) Practical quantum metrology where the underlying evolution of quantum probes may change from a unitary dynamics to an open system dynamics,owing to the inevitable decoherence during the quantum sensing operation. For various kinds of quantum multiple channels, the corresponding quantum channel Fisher information is derived. To demonstrate the results, some illustrative examples are given.