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Chin. Phys. B, 2023, Vol. 32(4): 040603    DOI: 10.1088/1674-1056/ac8721
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Feedback control and quantum error correction assisted quantum multi-parameter estimation

Hai-Yuan Hong(洪海源)1,†, Xiu-Juan Lu(鲁秀娟)2,†, and Sen Kuang(匡森)1,‡
1 Department of Automation, University of Science and Technology of China, Hefei 230027, China;
2 Department of Mechanical Engineering, The University of Hong Kong, Hong Kong 999077, China
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.
Keywords:  quantum multi-parameter estimation      feedback control      quantum error correction      Heisenberg limit  
Received:  13 April 2022      Revised:  29 July 2022      Accepted manuscript online:  05 August 2022
PACS:  06.20.-f (Metrology)  
  03.65.Yz (Decoherence; open systems; quantum statistical methods)  
  03.67.Pp (Quantum error correction and other methods for protection against decoherence)  
  03.67.-a (Quantum information)  
Fund: Project supported by the National Natural Science Foundation of China (Grant No. 61873251).
Corresponding Authors:  Sen Kuang     E-mail:

Cite this article: 

Hai-Yuan Hong(洪海源), Xiu-Juan Lu(鲁秀娟), and Sen Kuang(匡森) Feedback control and quantum error correction assisted quantum multi-parameter estimation 2023 Chin. Phys. B 32 040603

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