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Is it possible to recover Heisenberg limit by collecting information from memory environment

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Abstract

In quantum metrology, by using entangled probes, Heisenberg limit (HL), which surpasses the standard quantum limit (SQL) with uncorrelated probes, can be attained in the absence of noise. However, the entangled states are fragile in the environment. Even small amount of noise greatly reduces the precision limit. Recent results show that the magnitude of the reduced precision limit is determined by the direction of Hamiltonian which depends on the parameter to be estimated in comparison with the direction of noise. Especially, in parallel case, the precision limit becomes SQL-like. Here, we demonstrate that just in parallel case, the parameter to be estimated has clearly imprints on the “small” changed environment after proper measurements. Though the precision limit of the measures on the probe system itself becomes SQL-like, one kept the results of former measurements can collect the information of the parameter by choosing detector with proper initial state and proper interaction Hamiltonian and measuring the detector after the detector-environment evolution. The precision limit becomes HL-like after proper detector-environment evolution time.

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Fig. 1

Data availability statement

Data sharing not applicable to this article as no datasets were generated or analyzed during the current study.

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Acknowledgements

We thank H. Yu, P. Wu, J. Hu, Y. Zhou, J. Zhang, Q. Pan for helpful discussions. We thank X. Sun for discussions on numerical calculations. This work was supported by the National Natural Science Foundation of China under Grants No. 12165003, the special funding of Guiyang science and technology bureau and Guiyang University[GYU-KY-(2022)].

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  1. School of Electronic and Communication Engineering, Guiyang University, Guiyang, 550005, Guizhou, China

    Yao Jin

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Jin, Y. Is it possible to recover Heisenberg limit by collecting information from memory environment. Quantum Inf Process 22, 379 (2023). https://doi.org/10.1007/s11128-023-04140-9

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