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

doi:10.3969/j.issn.1000-5641.2024.03.010

Abstract

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

CLC Number:

O412

Jie ZENG, Chunhua YUAN. Research on the overestimation of sensitivity in lossy SU(2) and SU(1,1) interferometers[J]. Journal of East China Normal University(Natural Science), 2024, 2024(3): 91-100.

Figures/Tables 3

References 25

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-DOBRZAŃSKI R, KOŁODYŃSKI J, GUŢĂ 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-DOBRZAŃSKI 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.