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Quantum parameter estimation is one of the most important applications in quantum metrology. The basic theory of quantum parameter estimation－quantum Cramer-Rao bound－shows that the precision limit of quantum parameter estimation is directly related to quantum Fisher information. Therefore quantum Fisher information is extremely important in the quantum parameter estimation. In this paper we use quantum parameter estimation theory to estimate the coupling constant of the Jaynes-Cummings model with large detuning. The initial probing state is the direct product state of qubit and radiation field in which Fock state, thermal state and coherent state are taken into account respectively. We calculate the quantum Fisher information of the hybrid system as well as qubit and radiation field for each probing state after the parameter evolution under the Hamiltonian of the Jaynes-Cummings model with large detuning. The results show that the quantum Fisher information increases monotonically with the average photon number increasing. The optimal detection state is that when the qubit system is in the equal weight superposition of the ground and the excited state, at this time the quantum Fisher information always reaches a maximum value, When the radiation field of probing state is Fock state or the thermal state, the information about the estimated parameter is included only in the qubit. The estimation accuracy of the coupling constant with thermal state or coherent state is higher than that with Fock state.
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Keywords:
- quantum Fisher information /
- parameter estimation /
- quantum Cramer-Rao bound /
- Jaynes-Cummings model
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Google Scholar
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Jing X X 2016 Ph. D. Dissertation (Hangzhou: Zhejiang University) (in Chinese)
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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图 1 光场为Fock态时QFI随不同变量的变化(
${H_{{\rm{q}}1}}(\varOmega ) = {H_1}(\varOmega )$ ) (a)平均光子数$ \bar n_1 $ ; (b) θFigure 1. Variation of QFI with different variables when the radiation field is a Fock state (
${H_{{\rm{q}}1}}(\varOmega ) = {H_1}(\varOmega )$ ): (a) The average photon number,${\bar n_1}$ ; (b) θ.
图 2 光场为热态时QFI随不同变量的变化(
${H_{{\rm{q}}2}}(\varOmega ) = {H_2}(\varOmega )$ ) (a)平均光子数${\bar n_2}$ ; (b) θFigure 2. Variation of QFI with different variables when the radiation field is a thermal state (
${H_{{\rm{q}}2}}(\varOmega ) = {H_2}(\varOmega )$ ): (a) The average photon number,${\bar n_2}$ ; (b) θ.
图 3 腔场为相干态时QFI随不同变量的变化 (a)平均光子数
${\bar n_3}$ ; (b) θFigure 3. Variation of QFI with different variables when the radiation field is a coherent state: (a) The average photon number,
${\bar n_3}$ ; (b) the θ.
图 4
${H_1}(\varOmega )$ ,${H_2}(\varOmega )$ 和${H_3}(\varOmega )$ 随不同变量的变化 (a) 平均光子数$ \bar n $ ; (b) θFigure 4. Variation of the
${H_1}(\varOmega )$ ,${H_2}(\varOmega )$ and${H_3}(\varOmega )$ with different variables: (a) The average photon number,$ \bar n $ ; (b) θ. -
[1] Pang S S, Brun T A 2014 Phys. Rev. A 90 022117
Google Scholar
[2] 井晓幸 2016 博士学位论文 (杭州: 浙江大学)
Jing X X 2016 Ph. D. Dissertation (Hangzhou: Zhejiang University) (in Chinese)
[3] Genoni M G, Giorda P, Matteo G A P 2008 Phys. Rev. A 78 032303
Google Scholar
[4] Brida G, Degiovanni I, Florio A, Genovese M, Giorda P, Meda A, Matteo G A P, Shurupov A 2010 Phys. Rev. Lett. 104 100501
Google Scholar
[5] Giovannetti V, Lloyd S, Maccone L 2006 Phys. Rev. Lett. 96 010401
Google Scholar
[6] Monras A 2006 Phys. Rev. A 73 0338821
[7] Genoni M G, Olivares S, Matteo G A P 2011 Phys. Rev. Lett. 106 153603
Google Scholar
[8] Monras A, Matteo G A P 2007 Phys. Rev. Lett. 98 160401
Google Scholar
[9] Genoni M G, Invernizzi C, Matteo G A P 2009 Phys. Rev. A 80 033842
Google Scholar
[10] Lu X M, Wang X G 2021 Phys. Rev. Lett. 126 120503
Google Scholar
[11] Matteo G A P 2008 Int. J. Quant. Inf. 0804 2981
[12] Helstrom C W 1967 Phys. Lett. A 25 101
Google Scholar
[13] Yuen H P, Lax M 1973 IEEE Trans. Inf. Th. 19 740
Google Scholar
[14] Helstrom C W, Kennedy R S 1974 IEEE Trans. Inf. Th. 20 16
Google Scholar
[15] Braunstein S, Caves C 1994 Phys. Rev. Lett. 72 3439
Google Scholar
[16] Braunstein S, Caves C, Milburn G 1996 Ann. Phys. 247 135
Google Scholar
[17] Fisher R A 1925 Proc. Camb. Phil. Soc. 22 700
Google Scholar
[18] Helstrom C W 1969 J. Stat. Phys. 1 231
Google Scholar
[19] Holevo A S 1982 Probabilistic and Statistical Aspects of Quantum Theory (North Holland Amsterdam) pp52–96, 160–168
[20] Holevo A S 2001 Statistical Structure of Quantum Theory (Berlin, Heidelberg: Springer) pp45–70
[21] Pezze L, Smerzi A, Oberthaler M K, Schmied R, Treutlein P 2018 Rev. Mod. Phys. 90 035005
Google Scholar
[22] Gabbrielli M 2018 arXiv: 1810.10537 [quant-ph]
[23] Pezze' L, Smerzi A 2014 arXiv: 1411.5164 [quant-ph]
[24] 任志红, 李岩, 李艳娜, 李卫东 2019 68 040601
Google Scholar
Ren Z H, Li Y, LiY N, Li W D 2019 Acta Phys. Sin. 68 040601
Google Scholar
[25] Royfriened B 1998 Physics from Fisher Information (Cambridge: Cambridge University Press) pp22–62
[26] Liu J, Jing X X, Zhong W, Wang X G 2014 Commun. Theor. Phys. 61 45
Google Scholar
[27] Liu J, Yuan H D, Lu X M, Wang X G 2020 J. Phys. A:Math. Theor. 53 023001
Google Scholar
[28] Watanabe D Y 2014 Formulation of Uncertainty Relation Between Error and Disturbance in Quantum Measurement by Using Quantum Estimation Theory (Tokyo: Springer Theses) pp19–44
[29] Genoni M G, Tufarelli T 2019 Phys. A:Math. Theor. 52 434002
Google Scholar
[30] Monras A 2006 Phys. Rev. A 73 033821
Google Scholar
[31] Smirne A, Kolodynski J, Huelga S F, Dobrzanski R D 2016 Phys. Rev. Lett. 116 120801
Google Scholar
[32] Pirandola S, Lupo C 2017 Phys. Rev. Lett. 118 100502
Google Scholar
[33] Lupo C, Pirandola S 2016 Phys. Rev. Lett. 117 190802
Google Scholar
[34] Invernizzi C, Korbman M, Venuti L C, Matteo G A P 2008 Phys. Rev. A 78 042106
Google Scholar
[35] Schneiter F, Qvarfort S, Serafini A, Xuereb A, Braun D, Rätzel D, Bruschi D E, 2020 Phys. Rev. A. 101 033834
Google Scholar
[36] Sanavio C, Bernad J Z, Xuereb A 2020 Phys. Rev. A 102 013508
[37] Genoni M G, Invernizzi C 2012 Eur. Phys. J. Spec. 10 1140
[38] Gerry C, Knight P 2005 Introductory Quantum Optics (Cambridge: Cambridge University Press) pp25–27, 105–107
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