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Chin. Phys. B, 2024, Vol. 33(6): 060304    DOI: 10.1088/1674-1056/ad3430
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Enhancing quantum metrology for multiple frequencies of oscillating magnetic fields by quantum control

Xin Lei(雷昕), Jingyi Fan(范静怡), and Shengshi Pang(庞盛世)†
School of Physics, Sun Yat-sen University, Guangzhou 510275, China
Abstract  Quantum multi-parameter estimation has recently attracted increased attention due to its wide applications, with a primary goal of designing high-precision measurement schemes for unknown parameters. While existing research has predominantly concentrated on time-independent Hamiltonians, little has been known about quantum multi-parameter estimation for time-dependent Hamiltonians due to the complexity of quantum dynamics. This work bridges the gap by investigating the precision limit of multi-parameter quantum estimation for a qubit in an oscillating magnetic field model with multiple unknown frequencies. As the well-known quantum Cramér-Rao bound is generally unattainable due to the potential incompatibility between the optimal measurements for different parameters, we use the most informative bound instead which is always attainable and equivalent to the Holevo bound in the asymptotic limit. Moreover, we apply additional Hamiltonian to the system to engineer the dynamics of the qubit. By utilizing the quasi-Newton method, we explore the optimal schemes to attain the highest precision for the unknown frequencies of the magnetic field, including the simultaneous optimization of initial state preparation, the control Hamiltonian and the final measurement. The results indicate that the optimization can yield much higher precisions for the field frequencies than those without the optimizations. Finally, we study the robustness of the optimal control scheme with respect to the fluctuation of the interested frequencies, and the optimized scheme exhibits superior robustness to the scenario without any optimization.
Keywords:  quantum metrology      multi-parameter estimation      quantum control  
Received:  23 January 2024      Revised:  04 March 2024      Accepted manuscript online:  15 March 2024
PACS:  03.65.Ta (Foundations of quantum mechanics; measurement theory)  
  03.67.-a (Quantum information)  
Fund: Project supported by the National Natural Science Foundation of China (Grant No. 12075323).
Corresponding Authors:  Shengshi Pang     E-mail:  pangshsh@mail.sysu.edu.cn

Cite this article: 

Xin Lei(雷昕), Jingyi Fan(范静怡), and Shengshi Pang(庞盛世) Enhancing quantum metrology for multiple frequencies of oscillating magnetic fields by quantum control 2024 Chin. Phys. B 33 060304

[1] Holevo A 2011 Probabilistic and Statistical Aspects of Quantum Theory
[2] Helstrom C W 1969 Journal of Statistical Physics 1 231
[3] Braunstein S L and Caves C M 1994 Phys. Rev. Lett. 72 3439
[4] Huelga S F, Macchiavello C, Pellizzari T, Ekert A K, Plenio M B and Cirac J I 1997 Phys. Rev. Lett. 79 3865
[5] Niu C and Yu S 2024 Chin. Phys. B 33 20304
[6] Liu J, Lu X M, Sun Z and Wang X 2016 J. Phys. A: Math. Theor. 49 115302
[7] Liu J and Yuan H 2017 Phys. Rev. A 96 042114
[8] Liu J and Yuan H 2017 Phys. Rev. A 96 012117
[9] Xu H, Li J, Liu L, Wang Y, Yuan H and Wang X 2019 npj Quantum Information 5 1
[10] Zhou S, Zhang M, Preskill J and Jiang L 2018 Nat. Commun. 9 78
[11] Zhou S and Jiang L 2020 Phys. Rev. Res. 2 013235
[12] Dür W, Skotiniotis M, Fr öwis F and Kraus B 2014 Phys. Rev. Lett. 112 080801
[13] Kessler E M, Lovchinsky I, Sushkov A O and Lukin M D 2014 Phys. Rev. Lett. 112 150802
[14] Unden T, Balasubramanian P, Louzon D, Vinkler Y, Plenio M B, Markham M, Twitchen D, Stacey A, Lovchinsky I, Sushkov A O, Lukin M D, Retzker A, Naydenov B, McGuinness L P and Jelezko F 2016 Phys. Rev. Lett. 116 230502
[15] Tan K C, Omkar S and Jeong H 2019 Phys. Rev. A 100 022312
[16] Mahmud K W, Tiesinga E and Johnson P R 2014 Phys. Rev. A 90 041602
[17] Pang S and Jordan A N 2017 Nat. Commun. 8 14695
[18] Yuan H 2016 Phys. Rev. Lett. 117 160801
[19] Hou Z, Jin Y, Chen H, Tang J F, Huang C J, Yuan H, Xiang G Y, Li C F and Guo G C 2021 Phys. Rev. Lett. 126 070503
[20] Wan K and Lasenby R 2022 Phys. Rev. Res. 4 033092
[21] Yang J, Pang S, Chen Z, Jordan A N and del Campo A 2022 Phys. Rev. Lett. 128 160505
[22] Hong H, Lu X and Kuang S 2023 Chin. Phys. B 32 40603
[23] Valeri M, Polino E, Poderini D, Gianani I, Corrielli G, Crespi A, Osellame R, Spagnolo N and Sciarrino F 2020 npj Quantum Information 6 92
[24] Markiewicz M, Pandit M and Laskowski W 2021 Sci. Rep. 11 15669
[25] Xia B, Huang J, Li H, Wang H and Zeng G 2023 Nat. Commun. 14 1021
[26] Yin P, Zhao X, Yang Y, Guo Y, Zhang W H, Li G C, Han Y J, Liu B H, Xu J S, Chiribella G, Chen G, Li C F and Guo G C 2023 Nat. Phys. 19 1122
[27] Leibfried D, Barrett M D, Schaetz T, Britton J, Chiaverini J, Itano W M, Jost J D, Langer C and Wineland D J 2004 Science 304 1476
[28] Eisenberg H S, Hodelin J F, Khoury G and Bouwmeester D 2005 Phys. Rev. Lett. 94 090502
[29] Chen G, Zhang L, Zhang W H, Peng X X, Xu L, Liu Z D, Xu X Y, Tang J S, Sun Y N, He D Y, Xu J S, Zhou Z Q, Li C F and Guo G C 2018 Phys. Rev. Lett. 121 060506
[30] Treps N, Grosse N, Bowen W P, Fabre C, Bachor H A and Lam P K 2003 Science 301 940
[31] Morris P A, Aspden R S, Bell J E C, Boyd R W and Padgett M J 2015 Nat. Commun. 6 5913
[32] Casacio C A, Madsen L S, Terrasson A, Waleed M, Barnscheidt K, Hage B, Taylor M A and Bowen W P 2021 Nature 594 201
[33] Taylor M A, Janousek J, Daria V, Knittel J, Hage B, Bachor H A and Bowen W P 2013 Nat. Photon. 7 229
[34] Hou Z, Tang J F, Chen H, Yuan H, Xiang G Y, Li C F and Guo G C 2021 Sci. Adv. 7 eabd2986
[35] Xiao T, Fan J and Zeng G 2022 npj Quantum Information 8 2
[36] Nagata T, Okamoto R, O’Brien J L, Sasaki K and Takeuchi S 2007 Science 316 726
[37] Resch K J, Pregnell K L, Prevedel R, Gilchrist A, Pryde G J, O’Brien J L and White A G 2007 Phys. Rev. Lett. 98 223601
[38] 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
[39] Cramér H 2016 Mathematical Methods of Statistics (PMS-9), Vol. 9 (Princeton University Press)
[40] Giovannetti V, Lloyd S and Maccone L 2011 Nat. Photon. 5 222
[41] Giovannetti V, Lloyd S and Maccone L 2006 Phys. Rev. Lett. 96 010401
[42] Řehaček J, Hradil Z, Stoklasa B, Paúr M, Grover J, Krzic A and Sánchez-Soto L L 2017 Phys. Rev. A 96 062107
[43] Shih Y 2007 IEEE J. Select. Top. Quantum Electron. 13 1016
[44] Degen C L, Reinhard F and Cappellaro P 2017 Rev. Mod. Phys. 89 035002
[45] Shabani A, Mohseni M, Lloyd S, Kosut R L and Rabitz H 2011 Phys. Rev. A 84 012107
[46] Cole J H, Greentree A D, Oi D K L, Schirmer S G, Wellard C J and Hollenberg L C L 2006 Phys. Rev. A 73 062333
[47] Zhang J and Sarovar M 2014 Phys. Rev. Lett. 113 080401
[48] Wang Y, Dong D, Qi B, Zhang J, Petersen I R and Yonezawa H 2018 IEEE Trans. Autom. Control 63 1388
[49] Lu X M, Ma Z and Zhang C 2020 Phys. Rev. A 101 022303
[50] Helstrom C W 1967 Phys. Lett. A 25 101
[51] Yuen H and Lax M 1973 IEEE Trans. Inform. Theory 19 740
[52] Belavkin V P 1976 Theor. Math. Phys. 26 213
[53] Suzuki J 2019 Entropy 21 703
[54] Albarelli F, Barbieri M, Genoni M G and Gianani I 2020 Phys. Lett. A 384 126311
[55] Ragy S, Jarzyna M and Demkowicz-Dobrzański R 2016 Phys. Rev. A 94 052108
[56] Humphreys P C, Barbieri M, Datta A and Walmsley I A 2013 Phys. Rev. Lett. 111 070403
[57] Szczykulska M, Baumgratz T and Datta A 2016 Adv. Phys.: X 1 621
[58] Baumgratz T and Datta A 2016 Phys. Rev. Lett. 116 030801
[59] Gagatsos C N, Branford D and Datta A 2016 Phys. Rev. A 94 042342
[60] Yao Y, Ge L, Xiao X, Wang X G and Sun C P 2014 Phys. Rev. A 90 022327
[61] Zhang Y R and Fan H 2014 Phys. Rev. A 90 043818
[62] Yao Y, Ge L, Xiao X, Wang X and Sun C P 2014 Phys. Rev. A 90 062113
[63] Knott P A, Proctor T J, Hayes A J, Ralph J F, Kok P and Dunningham J A 2016 Phys. Rev. A 94 062312
[64] Berry D W, Tsang M, Hall M J W and Wiseman H M 2015 Phys. Rev. X 5 031018
[65] Yue J D, Zhang Y R and Fan H 2014 Sci. Rep. 4 5933
[66] Yuan H and Fung C H F 2015 Phys. Rev. Lett. 115 110401
[67] Xu H, Wang L, Yuan H and Wang X 2021 Phys. Rev. A 103 042615
[68] Khaneja N, Reiss T, Kehlet C, Schulte-Herbrüggen T and Glaser S J 2005 Journal of Magnetic Resonance 172 296
[69] William H. Press, Saul A Teukolsky, William T Vetterling and Brian P Flannery 1992 Numerical Recipes in C: The Art of Scientific Computing, 2nd edn. (USA: Cambridge University Press)
[70] Care C M 1983 Phys. Bull. 34 395
[71] Suzuki J, Yang Y and Hayashi M 2020 J. Phys. A: Math. Theor. 53 453001
[72] Suzuki J 2020 J. Phys. A: Math. Theor. 53 264001
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