Optimal initial states for quantum parameter estimation based on Jaynes–Cummings model [Invited]

Liwen Qiao; Jia-Xin Peng; Baiqiang Zhu; Weiping Zhang; Keye Zhang

doi:10.3788/COL202321.102701

Chinese Optics Letters, Volume. 21, Issue 10, 102701(2023)

Optimal initial states for quantum parameter estimation based on Jaynes–Cummings model [Invited]

Liwen Qiao¹, Jia-Xin Peng^1,2, Baiqiang Zhu^1,2, Weiping Zhang^2,3,4,5, and Keye Zhang^1,2、*

¹Quantum Institute for Light and Atoms, State Key Laboratory of Precision Spectroscopy, Department of Physics, School of Physics and Electronic Science, East China Normal University, Shanghai 200062, China

²Shanghai Branch, Hefei National Laboratory, Shanghai 201315, China

³School of Physics and Astronomy, and Tsung-Dao Lee Institute, Shanghai Jiao Tong University, Shanghai 200240, China

⁴Shanghai Research Center for Quantum Sciences, Shanghai 201315, China

⁵Collaborative Innovation Center of Extreme Optics, Shanxi University, Taiyuan 030006, China

show less

References(51)

[1] C. L. Degen, F. Reinhard, P. Cappellaro. Quantum sensing. Rev. Mod. Phys., 89, 035002(2017).

[2] V. Giovannetti, S. Lloyd, L. Maccone. Advances in quantum metrology. Nat. Photonics, 5, 222(2011).

[3] J. Liu, H. Yuan, X.-M. Lu, X. Wang. Quantum fisher information matrix and multiparameter estimation. J. Phys. A, 53, 023001(2020).

[4] R. A. Fisher. Theory of Statistical Estimation, 22, 700(1925).

[5] C. W. Helstrom. Quantum detection and estimation theory. J. Stat. Phys., 1, 231(1969).

[6] A. S. Holevo. Probabilistic and Statistical Aspects of Quantum Theory(2011).

[7] M. G. A. Paris. Quantum estimation for quantum technology. Int. J. Quantum Inf., 7, 125(2009).

[8] R. Demkowicz-Dobrzański, M. Jarzyna, J. Kołodyński. Quantum limits in optical interferometry. Prog. Opt., 60, 345(2015).

[9] X.-X. Jing, J. Liu, W. Zhong, X.-G. Wang. Quantum fisher information of entangled coherent states in a lossy Mach–Zehnder interferometer. Commun. Theor. Phys., 61, 115(2014).

[10] S. Pang, T. A. Brun. Quantum metrology for a general Hamiltonian parameter. Phys. Rev. A, 90, 022117(2014).

[11] X. Yu, X. Zhao, L. Shen, Y. Shao, J. Liu, X. Wang. Maximal quantum fisher information for phase estimation without initial parity. Opt. Express, 26, 16292(2018).

[12] M. G. Genoni, S. Olivares, M. G. A. Paris. Optical phase estimation in the presence of phase diffusion. Phys. Rev. Lett., 106, 153603(2011).

[13] U. Dorner, R. Demkowicz-Dobrzanski, B. J. Smith, J. S. Lundeen, W. Wasilewski, K. Banaszek, I. A. Walmsley. Optimal quantum phase estimation. Phys. Rev. Lett., 102, 040403(2009).

[14] Z. Hou, Y. Jin, H. Chen, J.-F. Tang, C.-J. Huang, H. Yuan, G.-Y. Xiang, C.-F. Li, G.-C. Guo. “Super-Heisenberg” and Heisenberg scalings achieved simultaneously in the estimation of a rotating field. Phys. Rev. Lett., 126, 070503(2021).

[15] Z. Hou, J.-F. Tang, H. Chen, H. Yuan, G.-Y. Xiang, C.-F. Li, G.-C. Guo. Zero–trade-off multiparameter quantum estimation via simultaneously saturating multiple Heisenberg uncertainty relations. Sci. Adv., 7, eabd2986(2021).

[16] C. Sanavio, J. Z. Bernád, A. Xuereb. Fisher-information-based estimation of optomechanical coupling strengths. Phys. Rev. A, 102, 013508(2020).

[17] Z. Sun, J. Ma, X.-M. Lu, X. Wang. Fisher information in a quantum-critical environment. Phys. Rev. A, 82, 022306(2010).

[18] K. Sala, T. Doicin, A. D. Armour, T. Tufarelli. Quantum estimation of coupling strengths in driven-dissipative optomechanics. Phys. Rev. A, 104, 033508(2021).

[19] J. Yang, S. Pang, Y. Zhou, A. N. Jordan. Optimal measurements for quantum multiparameter estimation with general states. Phys. Rev. A, 100, 032104(2019).

[20] A. Carollo, B. Spagnolo, A. A. Dubkov, D. Valenti. On quantumness in multi-parameter quantum estimation. J. Stat. Mech., 2019, 094010(2019).

[21] M. Szczykulska, T. Baumgratz, A. Datta. Multi-parameter quantum metrology. Adv. Phys. X, 1, 621(2016).

[22] R. Demkowicz-Dobrzański, W. Górecki, M. Guță. Multi-parameter estimation beyond quantum Fisher information. J. Phys. A, 53, 363001(2020).

[23] T. J. Proctor, P. A. Knott, J. A. Dunningham. Multiparameter estimation in networked quantum sensors. Phys. Rev. Lett., 120, 080501(2018).

[24] J. J. Meyer, J. Borregaard, J. Eisert. A variational toolbox for quantum multi-parameter estimation. npj Quantum Inf., 7, 89(2021).

[25] M. Tsang, R. Nair, X.-M. Lu. Quantum theory of superresolution for two incoherent optical point sources. Phys. Rev. X, 6, 031033(2016).

[26] K. Liang, S. Wadood, A. N. Vamivakas. Quantum Fisher information for estimating N partially coherent point sources. Opt. Express, 31, 2726(2023).

[27] J. Shao, X.-M. Lu. Performance-tradeoff relation for locating two incoherent optical point sources. Phys. Rev. A, 105, 062416(2022).

[28] Y. Zhou, J. Yang, J. D. Hassett, S. M. H. Rafsanjani, M. Mirhosseini, A. N. Vamivakas, A. N. Jordan, Z. Shi, R. W. Boyd. Quantum-limited estimation of the axial separation of two incoherent point sources. Optica, 6, 534(2019).

[29] P. C. Humphreys, M. Barbieri, A. Datta, I. A. Walmsley. Quantum enhanced multiple phase estimation. Phys. Rev. Lett., 111, 070403(2013).

[30] J.-D. Yue, Y.-R. Zhang, H. Fan. Quantum-enhanced metrology for multiple phase estimation with noise. Sci. Rep., 4, 5933(2014).

[31] C. N. Gagatsos, D. Branford, A. Datta. Gaussian systems for quantum-enhanced multiple phase estimation. Phys. Rev. A, 94, 042342(2016).

[32] A. Z. Goldberg, I. Gianani, M. Barbieri, F. Sciarrino, A. M. Steinberg, N. Spagnolo. Multiphase estimation without a reference mode. Phys. Rev. A, 102, 022230(2020).

[33] Y. Yao, L. Ge, X. Xiao, X.-G. Wang, C.-P. Sun. Multiple phase estimation in quantum cloning machines. Phys. Rev. A, 90, 022327(2014).

[34] W. Vogel, D.-G. Welsch. Quantum Optics(2006).

[35] P. Meystre, M. Sargent III. Elements of Quantum Optics(2007).

[36] M. Yönaç, T. Yu, J. H. Eberly. Sudden death of entanglement of two Jaynes–Cummings atoms. J. Phys. B At. Mol. Opt. Phys., 39, S621(2006).

[37] A. K. Rajagopal, K. L. Jensen, F. W. Cummings. Quantum entangled supercorrelated states in the Jaynes–Cummings model. Phys. Lett. A, 259, 285(1999).

[38] S. J. Akhtarshenas, M. Farsi. Negativity as entanglement degree of the Jaynes–Cummings model. Phys. Scr., 75, 608(2007).

[39] J. Gea-Banacloche. Collapse and revival of the state vector in the Jaynes–Cummings model: an example of state preparation by a quantum apparatus. Phys. Rev. Lett., 65, 3385(1990).

[40] N. Metwally, M. Abdelaty, A.-S. Obada. Quantum teleportation via entangled states generated by the Jaynes–Cummings model. Chaos Solitons Fractals, 22, 529(2004).

[41] J.-M. Liu, B. Weng. Approximate teleportation of an unknown atomic state in the two-photon Jaynes–Cummings model. Physica A, 367, 215(2006).

[42] F. Mirmasoudi, S. Ahadpour. Dynamics super quantum discord and quantum discord teleportation in the Jaynes–Cummings model. J. Mod. Opt., 65, 730(2018).

[43] M. G. Genoni, C. Invernizzi. Optimal quantum estimation of the coupling constant of Jaynes–Cummings interaction. Eur. Phys. J. Spec. Top., 203, 49(2012).

[44] K. E. Anouz, A. E. Allati, A. Salah, F. Saif. Quantum Fisher information: probe to measure fractional evolution. Int. J. Theor. Phys., 59, 1460(2020).

[45] A. Houssaoui, K. E. Anouz, A. E. Allati. Study of quantum Fisher information matrix and multiparameter estimation for an atomic-field system. Eur. Phys. J. Plus, 138, 109(2023).

[46] V. Giovannetti, S. Lloyd, L. Maccone. Quantum metrology. Phys. Rev. Lett., 96, 010401(2006).

[47] D. C. Brody, E.-M. Graefe. Information geometry of complex Hamiltonians and exceptional points. Entropy, 15, 3361(2013).

[48] S. L. Braunstein, C. M. Caves, G. J. Milburn. Generalized uncertainty relations: theory, examples, and Lorentz invariance. Ann. Phys., 247, 135(1996).

[49] E. Merzbacher. Quantum Mechanics(1998).

[50] F. Schwabl. Quantum Mechanics(2007).

[51] T. Radożycki. A concise and universal method for deriving arbitrary paraxial and d’Alembertian cylindrical Gaussian-type light modes. Opt. Laser Technol., 147, 107670(2022).

Cited By

[1] Jia-Xin Peng, Baiqiang Zhu, Weiping Zhang, Keye Zhang.

[2] Jia-Xin Peng, Baiqiang Zhu, Weiping Zhang, Keye Zhang.

[3] 田博轩 Tian Boxuan, 侯志博 Hou Zhibo, 项国勇 Xiang Guoyong.

Tools

Get Citation

Copy Citation Text

Liwen Qiao, Jia-Xin Peng, Baiqiang Zhu, Weiping Zhang, Keye Zhang, "Optimal initial states for quantum parameter estimation based on Jaynes–Cummings model [Invited]," Chin. Opt. Lett. 21, 102701 (2023)

Download Citation

EndNote(RIS)BibTex Plain Text

Set citation alerts for article

Save article for my favorites

Paper Information

Category: Quantum Optics and Quantum Information

Received: Apr. 18, 2023

Accepted: May. 31, 2023

Published Online: Oct. 11, 2023

The Author Email: Keye Zhang (kyzhang@phy.ecnu.edu.cn)

DOI:10.3788/COL202321.102701

Topics

laser devices and laser physics

Lasers and Laser Optics

Laser physics

laser manufacturing

Instrumentation, Measurement and Metrology