华东师范大学学报（自然科学版） >

2024 , Vol. 2024 >Issue 3: 91 - 100

DOI: https://doi.org/10.3969/j.issn.1000-5641.2024.03.010

原子、分子和光物理

损耗SU(2)和SU(1,1)干涉仪中灵敏度过高估计的研究

  • 曾杰 ,
  • 袁春华
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  • 华东师范大学 物理与电子科学学院, 上海　200241

收稿日期: 2023-05-11

  网络出版日期: 2024-05-25

基金资助

国家自然科学基金 (11974116)

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Research on the overestimation of sensitivity in lossy SU(2) and SU(1,1) interferometers

  • Jie ZENG ,
  • Chunhua YUAN
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  • School of Physics and Electronic Science, East China Normal University, Shanghai　200241, China

Received date: 2023-05-11

  Online published: 2024-05-25

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摘要

基于损耗SU(2)和SU(1,1)干涉仪模型, 以干涉仪中的相位估值的为研究方向, 在理论上研究了与双参量相位估值相比, 进行单参量相位估值的时候存在的高估量子Fisher信息(quantum Fisher information, QFI)的一般表达式; 以相干态和压缩真空态输入为例, 数值分析了高估QFI随损耗系数或分束比的变化, 发现这时出现的高估QFI的消失和恢复现象是和分束比, 增益因子以及压缩振幅具有一定的关系. 通过调整分束比和损耗系数, 可获得最佳的灵敏度, 有利于在有损环境下进行量子精密测量.

关键词： 多参量估值; 损耗干涉仪模型; 量子Fisher信息矩阵

本文引用格式

曾杰 , 袁春华 . 损耗SU(2)和SU(1,1)干涉仪中灵敏度过高估计的研究[J]. 华东师范大学学报（自然科学版）, 2024 , 2024(3) : 91 -100 . DOI: 10.3969/j.issn.1000-5641.2024.03.010

Abstract

In this study, based on the lossy SU(2) and SU(1,1) interferometer models, phase estimation in interferometers was investigated. The general expression for the overestimated quantum Fisher information (QFI), which exists when performing single-parameter phase estimation compared to two-parameter phase estimation, was theoretically studied. In addition, the variation in the overestimated QFI with the loss factor or beam splitting ratio was numerically analyzed with the input of coherent and squeezed vacuum states, and the disappearance and recovery of the overestimated QFI was related to the beam splitting ratio, gain factor, and squeeze amplitude. By adjusting the beam splitting ratio and loss factor, the best sensitivity was obtained, which is beneficial for quantum precision measurements in lossy environments.

Key words： multiparameter estimation; lossy interferometer model; quantum Fisher information matrix

参考文献

1 LEE H, KOK P, DOWLING J P.. A quantum Rosetta stone for interferometry. Journal of Modern Optics, 2002, 49 (14/15): 2325- 2338.
2 BRAUNSTEIN S L, CAVES C M, MILBURN G J.. Generalized uncertainty relations: Theory, examples, and Lorentz invariance. Annals of Physics, 1996, 247 (1): 135- 173.
3 BRAUNSTEIN S L, CAVES C M.. Statistical distance and the geometry of quantum states. Physical Review Letters, 1994, 72 (22): 3439- 3443.
4 CAVES C M.. Quantum-mechanical noise in an interferometer. Physical Review D, 1981, 23 (8): 1693- 1708.
5 HELSTROM C W. Quantum detection and estimation theory [J]. Journal of Statistical Physics, 1969, 1(2): 231-252.
6 YURKE B, MCCALL S L, KLAUDER J R.. SU(2) and SU(1, 1) interferometers. Physical Review A, 1986, 33 (6): 4033- 4054.
7 YUE J D, ZHANG Y R, FAN H.. Quantum-enhanced metrology for multiple phase estimation with noise. Scientific Reports, 2014, 4 (1): 5933.
8 DEMKOWICZ-DOBRZA?SKI R, KO?ODY?SKI J, GU?? M.. The elusive Heisenberg limit in quantum-enhanced metrology. Nature Communications, 2012, 3 (1): 1063.
9 ESCHER B M, DE MATOS FILHO R L, DAVIDOVICH L.. General framework for estimating the ultimate precision limit in noisy quantum-enhanced metrology. Nature Physics, 2011, 7 (5): 406- 411.
10 DEMKOWICZ-DOBRZANSKI R, DORNER U, SMITH B J, et al.. Quantum phase estimation with lossy interferometers. Physical Review A, 2009, 80 (1): 013825.
11 GAO Y, LEE H.. Bounds on quantum multiple-parameter estimation with Gaussian state. The European Physical Journal D, 2014, 68, 347.
12 LIU J, JING X X, WANG X G.. Phase-matching condition for enhancement of phase sensitivity in quantum metrology. Physical Review A, 2013, 88 (4): 042316.
13 PINEL O, JIAN P, TREPS N, et al.. Quantum parameter estimation using general single-mode Gaussian states. Physical Review A, 2013, 88 (4): 040102.
14 SPARACIARI C, OLIVARES S, PARIS M G A.. Bounds to precision for quantum interferometry with Gaussian states and operations. Journal of the Optical Society of America B, 2015, 32 (7): 1354- 1359.
15 WANG X B, HIROSHIMA T, TOMITA A, et al.. Quantum information with Gaussian states. Physics Reports, 2007, 448 (1/2/3/4): 1- 111.
16 DEMKOWICZ-DOBRZAŃSKI R, JARZYNA M, KOŁODYŃSKI J. Chapter Four - Quantum Limits in Optical Interferometry [M]//Progress in Optics. [S.l.]: Elsevier Ltd., 2015, 60: 345-435.
17 TóTH G, APELLANIZ I.. Quantum metrology from a quantum information science perspective. Journal of Physics A, 2014, 47 (42): 424006.
18 JARZYNA M, DEMKOWICZ-DOBRZA?SKI R.. Quantum interferometry with and without an external phase reference. Physical Review A, 2012, 85 (1): 011801.
19 GONG Q K, LI D, YUAN C H, et al.. Phase estimation of phase shifts in two arms for an SU(1, 1) interferometer with coherent and squeezed vacuum states*. Chinese Physics B, 2017, 26 (9): 094205.
20 LI D, GARD B T, GAO Y, et al.. Phase sensitivity at the Heisenberg limit in an SU(1, 1) interferometer via parity detection. Physical Review A, 2016, 94 (6): 063840.
21 LIU J, YUAN H, LU X M, et al.. Quantum Fisher information matrix and multiparameter estimation. Journal of Physics A, 2020, 53 (2): 023001.
22 SZCZYKULSKA M, BAUMGRATZ T, DATTA A.. Multi-parameter quantum metrology. Advances in Physics: X, 2016, 1 (4): 621- 639.
23 PARIS M G A.. Quantum estimation for quantum technology. International Journal of Quantum Information, 2009, 7 (supp01): 125- 137.
24 YOU C L, ADHIKARI S, MA X P, et al.. Conclusive precision bounds for SU(1, 1) interferometers. Physical Review A, 2019, 99 (4): 042122.
25 TAKEOKA M, SESHADREESAN K P, YOU C L, et al.. Fundamental precision limit of a Mach-Zehnder interferometric sensor when one of the inputs is the vacuum. Physical Review A, 2017, 96 (5): 052118.
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