Parameter estimation in n-dimensional massless scalar field

doi:10.1088/1674-1056/ad1749

中国物理B ›› 2024, Vol. 33 ›› Issue (3): 30307-030307.doi: 10.1088/1674-1056/ad1749

Parameter estimation in n-dimensional massless scalar field

Ying Yang(杨颖)^1,† and Jiliang Jing(荆继良)²

1 Hunan Provincial Key Laboratory of Intelligent Sensors and Advanced Sensor Materials, School of Physics and Electronics, Hunan University of Science and Technology, Xiangtan 411201, China;
2 Department of Physics, Key Laboratory of Low Dimensional Quantum Structures and Quantum Control of Ministry of Education, and Synergetic Innovation Center for Quantum Effects and Applications, Hunan Normal University, Changsha 410081, Chin

收稿日期:2023-10-08 修回日期:2023-11-30 接受日期:2023-12-20 出版日期:2024-02-22 发布日期:2024-03-06
通讯作者: Ying Yang E-mail:yingyanghnust@163.com
基金资助:
Project supported by the National Natural Science Foundation of China (Grant Nos. 12105097 and 12035005) and the Science Research Fund of the Education Department of Hunan Province, China (Grant No. 23B0480).

Parameter estimation in n-dimensional massless scalar field

Ying Yang(杨颖)^1,† and Jiliang Jing(荆继良)²

1 Hunan Provincial Key Laboratory of Intelligent Sensors and Advanced Sensor Materials, School of Physics and Electronics, Hunan University of Science and Technology, Xiangtan 411201, China;
2 Department of Physics, Key Laboratory of Low Dimensional Quantum Structures and Quantum Control of Ministry of Education, and Synergetic Innovation Center for Quantum Effects and Applications, Hunan Normal University, Changsha 410081, Chin

Received:2023-10-08 Revised:2023-11-30 Accepted:2023-12-20 Online:2024-02-22 Published:2024-03-06
Contact: Ying Yang E-mail:yingyanghnust@163.com
Supported by:
Project supported by the National Natural Science Foundation of China (Grant Nos. 12105097 and 12035005) and the Science Research Fund of the Education Department of Hunan Province, China (Grant No. 23B0480).

摘要/Abstract

摘要： Quantum Fisher information (QFI) associated with local metrology has been used to parameter estimation in open quantum systems. In this work, we calculated the QFI for a moving Unruh-DeWitt detector coupled with massless scalar fields in n-dimensional spacetime, and analyzed the behavior of QFI with various parameters, such as the dimension of spacetime, evolution time, and Unruh temperature. We discovered that the QFI of state parameter decreases monotonically from 1 to 0 over time. Additionally, we noted that the QFI for small evolution times is several orders of magnitude higher than the QFI for long evolution times. We also found that the value of QFI decreases at first and then stabilizes as the Unruh temperature increases. It was observed that the QFI depends on initial state parameter θ, and F_θ is the maximum for θ=0 or θ=π, F_φ is the maximum for θ=π/2. We also obtain that the maximum value of QFI for state parameters varies for different spacetime dimensions with the same evolution time.

关键词: quantum Fisher information, parameter estimation, open quantum systems

Abstract: Quantum Fisher information (QFI) associated with local metrology has been used to parameter estimation in open quantum systems. In this work, we calculated the QFI for a moving Unruh-DeWitt detector coupled with massless scalar fields in n-dimensional spacetime, and analyzed the behavior of QFI with various parameters, such as the dimension of spacetime, evolution time, and Unruh temperature. We discovered that the QFI of state parameter decreases monotonically from 1 to 0 over time. Additionally, we noted that the QFI for small evolution times is several orders of magnitude higher than the QFI for long evolution times. We also found that the value of QFI decreases at first and then stabilizes as the Unruh temperature increases. It was observed that the QFI depends on initial state parameter θ, and F_θ is the maximum for θ=0 or θ=π, F_φ is the maximum for θ=π/2. We also obtain that the maximum value of QFI for state parameters varies for different spacetime dimensions with the same evolution time.

Key words: quantum Fisher information, parameter estimation, open quantum systems

中图分类号: (Decoherence; open systems; quantum statistical methods)

03.65.Yz

06.20.-f (Metrology) 03.65.Ta (Foundations of quantum mechanics; measurement theory)

Ying Yang(杨颖) and Jiliang Jing(荆继良). Parameter estimation in n-dimensional massless scalar field[J]. 中国物理B, 2024, 33(3): 30307-030307.

Ying Yang(杨颖) and Jiliang Jing(荆继良). Parameter estimation in n-dimensional massless scalar field[J]. Chin. Phys. B, 2024, 33(3): 30307-030307.

参考文献

[1] Isar A, Sandulescu A, Scutaru H, Stefanescu E and Scheid W 1994 Int. J. Mod. Phys. E 3 635
[2] Viola L, Knill E and Lloyd S 1999 Phys. Rev. Lett. 82 2417
[3] Rivas A and Huelga S F 2012 Open quantum systems (Berlin: Springer)
[4] Gorini V, Kossakowski A and Surdarshan E C G 1976 J. Math. Phys. 17 821
[5] Lindblad G 1976 Commun. Math. Phys. 48 119
[6] Lu X M, Wang X and Sun C P 2010 Phys. Rev. A 82 042103
[7] Jin Y and Yu H W 2015 Phys. Rev. A 91 022120
[8] Liu X, Jing J, Tian Z and Yao W 2021 Phys. Rev. D 103 125025
[9] Feng J and Zhang J J 2022 Phys. Lett. B 827 136992
[10] Yang Y, Jing J L and Tian Z H 2022 Eur. Phys. J. C 82 1
[11] Yang Y, Zhang Y Q, Jia C X and Jing J L 2023 Quantum Inf. Process. 22 1
[12] Giovannetti V, Lloyd S and Maccone L 2004 Science 306 1330
[13] Giovannetti V, Lloyd S and Maccone L 2006 Phys. Rev. Lett. 96 010401
[14] Chin A W, Huelga S F and Plenio M B 2012 Phys. Rev. Lett. 109 233601
[15] Demkowicz-Dobrza'nski R and Maccone L 2014 Phys. Rev. Lett. 113 250801
[16] Liu J, Zhang M, Chen H, Wang L and Yuan H 2022 Advanced Quantum Technologies 5 2100080
[17] Barbieri M 2022 PRX Quantum 3 010202
[18] Yang J, Pang S, Chen Z, Jordan A N and Del Campo A 2022 Phys. Rev. Lett. 128 160505
[19] Giovannetti V, Lloyd S and Maccone L 2011 Nat. Photonics 5 222
[20] Fisher R A 1925 Theory of statistical estimation (Cambridge: Cambridge University Press)
[21] Petz D and Ghinea C 2011 Introduction to quantum Fisher information (Singapore: World Scientific)
[22] Mathew G, Silva S L L, Jain A, et al. 2020 Phys. Rev. Res. 2 043329
[23] Liu J, Yuan H, Lu X M and Wang X 2020 J. Phys. A 53 023001
[24] Wang J, Tian Z, Jing J and Fan H 2014 Sci. Rep 4 7195
[25] Hyllus P, Laskowski W, Krischek R, et al. 2012 Phys. Rev. A 85 022321
[26] Li N and Luo S 2013 Phys. Rev. A 88 014301
[27] Wang T L, Wu L N, Yang W, Jin G R, Lambert N and Nori F 2014 New J. Phys. 16 063039
[28] Marzolino U and Prosen T 2017 Phys. Rev. B 96 104402
[29] Dell'Anna F, Pradhan S, Boschi C D E and Ercolessi E 2023 Phys. Rev. B 108 144414
[30] Hauke P, Heyl M, Tagliacozzo L and Zoller P 2016 Nat. Phys. 12 778
[31] Zhang Y M, Li X W, Yang W and Jin G R 2013 Phys. Rev. A 88 043832
[32] Hu M L and Wang H F 2020 Annalen der Physik 532 1900378
[33] Ban M 2023 Phys. Lett. A 468 128749
[34] Martin-Martinez E, Montero M and del Rey M 2013 Phys. Rev. D 87 064038
[35] Fulling S A 1973 Phys. Rev. D 7 2850
[36] Unruh W G 1976 Phys. Rev. D 14 870
[37] Unruh W G 1984 Phys. Rev. D 29 1047
[38] Yang Y Y, Ye L and Wang D 2020 Annalen der Physik 532 2000062
[39] Louko J and Satz A 2008 Class. Quantum Grav 25 055012
[40] Zhou Y, Hu J and Yu H 2021 JHEP 2021 88
[41] Zhang J and Yu H 2020 Phys. Rev. D 102 065013
[42] Zhao Z, Pan Q and Jing J 2020 Phys. Rev. D 101 056014
[43] Takagi S 1986 Prog. Theor. Phys. Suppl. 88 1
[44] Sriramkumar L 2002 Mod. Phys. Lett. A 17 1059
[45] Yan J and Zhang B 2022 JHEP 2022 51
[46] Breuer H P and Petruccione F 2002 The theory of open quantum systems (Oxford: Oxford University Press)
[47] Cramér H 2016 Mathematical Methods of Statistics (Princeton: Princeton University)
[48] Braunstein S L and Caves C M 1994 Phys. Rev. Lett. 72 3439
[49] Helstrom C W 1967 Phys. Lett. A 25 101
[50] Zhong W, Sun Z, Ma J, Wang X and Nori F 2013 Phys. Rev. A 87 022337
[51] Jeffrey A and Zwillinger D 2007 Table of integrals, series, and products (Burlington: Elsevier)

Parameter estimation in n-dimensional massless scalar field

Parameter estimation in n-dimensional massless scalar field

RichHTML

PDF (PC)

赞

可视化

摘要/Abstract

引用本文

使用本文

参考文献

相关文章 15

Metrics

本文评价

推荐阅读 0

[1]	Chang Niu(牛畅) and Sixia Yu(郁司夏). Holevo bound independent of weight matrices for estimating two parameters of a qubit[J]. 中国物理B, 2024, 33(2): 20304-020304.
[2]	Ningzhe Zhang(张宁哲), Xiaopeng Yan(闫晓鹏), Minghui Lv(吕明慧), Xiumei Chen(陈秀梅), and Dingkun Huang(黄鼎琨). Parameter estimation method for a linear frequency modulation signal with a Duffing oscillator based on frequency periodicity[J]. 中国物理B, 2023, 32(8): 80701-080701.
[3]	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[J]. 中国物理B, 2023, 32(4): 40603-040603.
[4]	Yan-Ling Li(李艳玲), Yi-Bo Zeng(曾艺博), Lin Yao(姚林), and Xing Xiao(肖兴). Improving the teleportation of quantum Fisher information under non-Markovian environment[J]. 中国物理B, 2023, 32(1): 10303-010303.
[5]	Mengmeng Luo(罗萌萌), Wenxiao Liu(刘文晓), Yuetao Chen(陈悦涛), Shangbin Han(韩尚斌), and Shaoyan Gao(高韶燕). Environmental parameter estimation with the two-level atom probes[J]. 中国物理B, 2022, 31(5): 50304-050304.
[6]	Hao Luo(罗浩), Yi-Jun Wang(王一军), Wei Ye(叶炜), Hai Zhong(钟海), Yi-Yu Mao(毛宜钰), and Ying Guo(郭迎). Parameter estimation of continuous variable quantum key distribution system via artificial neural networks[J]. 中国物理B, 2022, 31(2): 20306-020306.
[7]	M Bagheri Harouni. Influences of spin-orbit interaction on quantum speed limit and entanglement of spin qubits in coupled quantum dots[J]. 中国物理B, 2021, 30(9): 90301-090301.
[8]	Dong Xie(谢东), Chunling Xu(徐春玲), and Anmin Wang(王安民). Quantum metrology with coherent superposition of two different coded channels[J]. 中国物理B, 2021, 30(9): 90304-090304.
[9]	Ke Wang(王珂), Xiaopeng Yan(闫晓鹏), Ze Li(李泽), Xinhong Hao(郝新红), and Honghai Yu(于洪海). Blind parameter estimation of pseudo-random binary code-linear frequency modulation signal based on Duffing oscillator at low SNR[J]. 中国物理B, 2021, 30(5): 50708-050708.
[10]	彭越兮, 孙克辉, 贺少波. Dynamics analysis of chaotic maps: From perspective on parameter estimation by meta-heuristic algorithm[J]. 中国物理B, 2020, 29(3): 30502-030502.
[11]	朱雯丽, 吴威, 罗洪刚. Effect of system-reservoir correlations on temperature estimation[J]. 中国物理B, 2020, 29(2): 20501-020501.
[12]	王晓岚, 任玉坤, 曾浩生. Dynamical control of population and entanglement for open Λ-type atoms by engineering the environment[J]. 中国物理B, 2019, 28(3): 30301-030301.
[13]	谢东, 徐春玲. Quantum estimation of detection efficiency with no-knowledge quantum feedback[J]. 中国物理B, 2018, 27(6): 60303-060303.
[14]	杨乐, 戴宏毅, 张明. Quantum parameter estimation in a spin-boson dephasing quantum system by periodical projective measurements[J]. 中国物理B, 2018, 27(4): 40601-040601.
[15]	黄江, 师文庆, 谢玉萍, 徐国保, 巫慧娴. Quantum metrology with a non-Markovian qubit system[J]. 中国物理B, 2018, 27(12): 120301-120301.