Feedback control and QEC assisted quantum multi-parameter estimation

Abstract Quantum metrology provides a fundamental limit on the precision of multi-parameter estimation, called the Heisenberg limit, which has been achieved in noiseless quantum systems. However, for systems subject to noises, it is hard to achieve this limit since noises are inclined to destroy quantum coherence and entanglement. In this paper, a combined control scheme with feedback and quantum error correction (QEC) is proposed to achieve the Heisenberg limit in the presence of spontaneous emission, where the feedback control is used to protect a stabilizer code space containing an optimal probe state and an additional control is applied to eliminate the measurement incompatibility among three parameters. Although an ancilla system is necessary for the preparation of the optimal probe state, our scheme does not require the ancilla system to be noiseless. In addition, the control scheme in this paper has a low-dimensional code space. For the three components of a magnetic field, it can achieve the highest estimation precision with only a 2-dimensional code space, while at least a 4-dimensional code space is required in the common optimal error correction protocols.