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Extension of Linear Response Regime in Weak-Value Amplification Technique |
Manchao Zhang1,2,3, Jie Zhang1,2,3, Wenbo Su1,2,3, Xueying Yang1,2,3, Chunwang Wu1,2,3, Yi Xie1,2,3, Wei Wu1,2,3, and Pingxing Chen1,2,3* |
1Institute for Quantum Science and Technology, College of Science, National University of Defense Technology, Changsha 410073, China 2Hunan Key Laboratory of Mechanism and Technology of Quantum Information, Changsha 410073, China 3Hefei National Laboratory, Hefei 230088, China
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Cite this article: |
Manchao Zhang, Jie Zhang, Wenbo Su et al 2023 Chin. Phys. Lett. 40 040301 |
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Abstract The achievable precision of parameter estimation plays a significant role in evaluating a strategy of metrology. In practice, one may employ approximations in a theoretical model development for simplicity, which, however, will cause systematic error and lead to a loss of precision. We derive the error of maximum likelihood estimation in the weak-value amplification technique where the linear approximation of the coupling parameter is used. We show that this error is positively related to the coupling strength and can be effectively suppressed by improving the Fisher information. Considering the roles played by weak values and initial meter states in the weak-value amplification, we also point out that the estimation error can be decreased by several orders of magnitude by averaging the estimations resulted from different initial meter states or weak values. These results are finally illustrated in a numerical example where an extended linear response regime to the parameter is observed.
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Received: 01 February 2023
Published: 02 April 2023
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PACS: |
03.67.-a
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(Quantum information)
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03.65.Ta
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(Foundations of quantum mechanics; measurement theory)
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03.65.-w
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(Quantum mechanics)
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[1] | Pezzè L and Smerzi A 2018 Rev. Mod. Phys. 90 035005 |
[2] | Tóth G and Apellaniz I 2014 J. Phys. A 47 424006 |
[3] | Braunstein S L and Caves C M 1994 Phys. Rev. Lett. 72 3439 |
[4] | Zhang L J, Datta A, and Walmsley I A 2015 Phys. Rev. Lett. 114 210801 |
[5] | Aharonov Y, Albert D Z, and Vaidman L 1988 Phys. Rev. Lett. 60 1351 |
[6] | Aharonov Y and Vaidman L 1990 Phys. Rev. A 41 11 |
[7] | Hosten O and Kwiat P 2008 Science 319 787 |
[8] | Dressel J, Malik M, Miatto F M, Jordan A N, and Boyd R W 2014 Rev. Mod. Phys. 86 307 |
[9] | Zhang J, Wu C W, Xie Y, Wu W, and Chen P X 2021 Chin. Phys. B 30 033201 |
[10] | Dixon P B, Starling D J, Jordan A N, and Howell J C 2009 Phys. Rev. Lett. 102 173601 |
[11] | Wu C W, Zhang J, Xie Y, Ou B Q, Chen T, Wu W, and Chen P X 2019 Phys. Rev. A 100 062111 |
[12] | Chen G, Aharon N, Sun Y N, Zhang Z H, Zhang W H, He D Y, Tang J S, Xu X Y, Kedem Y, Li C F, and Guo G C 2018 Nat. Commun. 9 93 |
[13] | Fang C, Huang J Z, Yu Y, Li Q, and Zeng G 2016 J. Phys. B 49 175501 |
[14] | Xu X Y, Kedem Y, Sun K, Vaidman L, Li C F, and Guo G C 2013 Phys. Rev. Lett. 111 033604 |
[15] | Li H J, Huang J Z, Yu Y et al. 2018 Appl. Phys. Lett. 112 231901 |
[16] | Egan P and Stone J A 2012 Opt. Lett. 37 4991 |
[17] | Viza G I, Martinez-Rincon J, Howland G A, Frostig H, Shomroni I, Dayan B, and Howell J C 2013 Opt. Lett. 38 2949 |
[18] | Xu L, Liu Z, Datta A, Knee G C, Lundeen J S, Lu Y Q, and Zhang L 2020 Phys. Rev. Lett. 125 080501 |
[19] | Kedem Y 2012 Phys. Rev. A 85 060102(R) |
[20] | Jordan A N, Martinez-Rincon J, and Howell J C 2014 Phys. Rev. X 4 011031 |
[21] | Knee G C and Gauger E M 2014 Phys. Rev. X 4 011032 |
[22] | Wu S J and Li Y 2011 Phys. Rev. A 83 052106 |
[23] | Koike T and Tanaka S 2011 Phys. Rev. A 84 062106 |
[24] | Turek Y, Kobayashi H, Akutsu T, Sun C P, and Shikano Y 2015 New J. Phys. 17 083029 |
[25] | Nakamura K, Nishizawa A, and Fujimoto M K 2012 Phys. Rev. A 85 012113 |
[26] | Pang S S, Alonso J R G, Brun T A, and Jordan A N 2016 Phys. Rev. A 94 012329 |
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