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
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 Fθ is the maximum for θ=0 or θ=π, Fφ 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.
(Foundations of quantum mechanics; measurement theory)
Fund: 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).
Corresponding Authors:
Ying Yang
E-mail: yingyanghnust@163.com
Cite this article:
Ying Yang(杨颖) and Jiliang Jing(荆继良) Parameter estimation in n-dimensional massless scalar field 2024 Chin. Phys. B 33 030307
[1] Isar A, Sandulescu A, Scutaru H, Stefanescu E and Scheid W 1994 Int. J. Mod. Phys. E3 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. A82 042103 [7] Jin Y and Yu H W 2015 Phys. Rev. A91 022120 [8] Liu X, Jing J, Tian Z and Yao W 2021 Phys. Rev. D103 125025 [9] Feng J and Zhang J J 2022 Phys. Lett. B827 136992 [10] Yang Y, Jing J L and Tian Z H 2022 Eur. Phys. J. C82 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 Science306 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 Technologies5 2100080 [17] Barbieri M 2022 PRX Quantum3 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. Photonics5 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. A53 023001 [24] Wang J, Tian Z, Jing J and Fan H 2014 Sci. Rep4 7195 [25] Hyllus P, Laskowski W, Krischek R, et al. 2012 Phys. Rev. A85 022321 [26] Li N and Luo S 2013 Phys. Rev. A88 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. B96 104402 [29] Dell'Anna F, Pradhan S, Boschi C D E and Ercolessi E 2023 Phys. Rev. B108 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. A88 043832 [32] Hu M L and Wang H F 2020 Annalen der Physik532 1900378 [33] Ban M 2023 Phys. Lett. A468 128749 [34] Martin-Martinez E, Montero M and del Rey M 2013 Phys. Rev. D87 064038 [35] Fulling S A 1973 Phys. Rev. D7 2850 [36] Unruh W G 1976 Phys. Rev. D14 870 [37] Unruh W G 1984 Phys. Rev. D29 1047 [38] Yang Y Y, Ye L and Wang D 2020 Annalen der Physik532 2000062 [39] Louko J and Satz A 2008 Class. Quantum Grav25 055012 [40] Zhou Y, Hu J and Yu H 2021 JHEP2021 88 [41] Zhang J and Yu H 2020 Phys. Rev. D102 065013 [42] Zhao Z, Pan Q and Jing J 2020 Phys. Rev. D101 056014 [43] Takagi S 1986 Prog. Theor. Phys. Suppl.88 1 [44] Sriramkumar L 2002 Mod. Phys. Lett. A17 1059 [45] Yan J and Zhang B 2022 JHEP2022 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. A25 101 [50] Zhong W, Sun Z, Ma J, Wang X and Nori F 2013 Phys. Rev. A87 022337 [51] Jeffrey A and Zwillinger D 2007 Table of integrals, series, and products (Burlington: Elsevier)
Altmetric calculates a score based on the online attention an article receives. Each coloured thread in the circle represents a different type of online attention. The number in the centre is the Altmetric score. Social media and mainstream news media are the main sources that calculate the score. Reference managers such as Mendeley are also tracked but do not contribute to the score. Older articles often score higher because they have had more time to get noticed. To account for this, Altmetric has included the context data for other articles of a similar age.
