Jaynes-Cummings Modelinde Çiftlenim Sabitinin Kuantum Tahmini

Durgun Duran

doi:10.35193/bseufbd.632771

Jaynes-Cummings Modelinde Çiftlenim Sabitinin Kuantum Tahmini

Abstract

Vazgeçilmez avantajlarıyla birlikte, kuantum Fisher bilişimi (QFI), bilinmeyen bir parametrenin değerini belirlemek ve çözünürlük hassasiyetini geliştirmek için anahtar özkaynaklardır. Bu çalışmada, biri Jaynes-Cummings kovuğunda diğeri ise tamamen izole edilmiş, uzaysal olarak ayrılmış iki atomun çiftlenim sabitine ilişkin olarak QFI dinamikleri incelenecek ve QFI’nın, en uygun tahmin için kuantum Cramér-Rao sınırı doyurulacak şekilde parametreler ayarlanarak maksimize edilebileceği gösterilecektir.

Keywords

kuantum parametre tahmini,kuantum Fisher bilişimi,Jaynes-Cummings modeli

References

[1] Giovannetti, V., Lloyd, S., Maccone, L. (2004). Quantum-Enhanced Measurements: Beating the Standard Quantum Limit. Science, 306, 1330-1336.
[2] Giovannetti, V., Lloyd, S., Maccone, L. (2006). Quantum Metrology. Phys. Rev. Lett., 96, 010401.
[3] Giovannetti, V., Lloyd, S., Maccone, L. (2011). Advances in quantum metrology. Nature Photon., 5, 222-229.
[4] Jaynes, E. T., Cummings, F. W. (1963). Comparison of quantum and semiclassical radiation theories with application to the beam maser. Proc. IEEE, 51(1), 89-109.
[5] Fisher, R. A. (1925). Theory of Statistical Estimation. Proc. Camb. Phil. Soc., 22(5), 700-725.
[6] Paris, M. G. A. (2009). Quantum estimation for quantum technology. Int. J. Quantum Inform., 07, 125-137.
[7] Petz, D., Ghinea, C. (2011). Introduction to quantum Fisher information. QP-PQ: Quantum Probability and White Noise Analysis 27, World Scientific, Chile, 261-281.
[8] Tóth, G., Apellaniz, I. (2014). Quantum metrology from a quantum information science perspective. J. Phys. A: Math. Theor. 47, 424006.

[9] Yönaç, M., Yu, T., Eberly, J. H. (2006). Sudden death of entanglement of two Jaynes-Cummings atoms. J. Phys. B: At. Mol. Opt. Phys., 39, S621-S625.
[10] Yu, T., Eberly, J. H. (2006). Sudden death of entanglement: classical noise effects. Opt. Commun., 264(2), 393-397.
[11] Li, Zhi-Jian., Li, Jun-Qi., Jin, Yan-Hong., Nie, Yi-Hang. (2007). Time evolution and transfer of entanglement between an isolated atom and a Jaynes-Cummings atom. J. Phys. B: At. Mol. Opt. Phys., 40, 3401-3411.
[12] Cramér, H. (1946). Mathematical Methods of Statistics, Princeton University Press, Princeton, 575.
[13] Rao, C. R. (1945). Information and the Accuracy Attainable in the Estimation of Statistical Parameters. Bulletin of the Calcutta Mathematical Society, 37, 81-89.
[14] Helstrom, C.W. (1976). Quantum Detection and Estimation Theory, Academic Press, INC., New York, 309.
[15] Holevo, A.S. (1982). Probabilistic and Statistical Aspects of Quantum Theory, North-Holland Publishing Company, Amsterdam, 312.
[16] Ragy, S., Jarzyna, M., Demkowicz-Dobrzánski, R. (2016). Compatibility in multiparameter quantum metrology. Phys. Rev. A, 94, 052108.
[17] Braunstein, S. L., Caves, C. M. (1994). Statistical distance and the geometry of quantum states. Phys. Rev. Lett., 72, 3439.
[18] Liu, J., Jing, X. X, Wang, X. (2013). Phase-matching condition for enhancement of phase sensitivity in quantum metrology. Phys. Rev. A, 88, 042316.
[19] Zhang, Y. M., Li, X. W., Yang, W., Jin. G. R. (2013). Quantum Fisher information of entangled coherent states in the presence of photon loss. Phys. Rev. A, 88, 043832.
[20] Liu, J., Jing, X. X., Zhong, W., Wang, X. G. (2014). Quantum Fisher Information for Density Matrices with Arbitrary Ranks. Commun. Theor. Phys., 61, 45-50.
[21] Jing, X. X., Liu, J., Zhong, W., Wang, X. (2014). Quantum Fisher Information of Entangled Coherent States in a Lossy Mach-Zehnder Interferometer. Commun. Theor. Phys., 61, 115-120.
[22] Liu, J., Yuan, H., Lu, X. M., Wang, X. G. Quantum Fisher information matrix and multiparameter estimation. arXiv:1907.08037.
[23] Boixo, S., Flammia, S. T., Caves, C. M., Geremia, J. M. (2007). Generalized Limits for Single-Parameter Quantum Estimation. Phys. Rev. Lett., 98, 090401.
[24] Liu, J., Jing, X. X., Wang, X. G. (2015). Quantum metrology with unitary parametrization processes. Sci. Rep., 5, 8565.
[25] Taddei, M. M., Escher, B. M., Davidovich, L. de Matos Filho, R. L. (2013). Quantum Speed Limit for Physical Processes. Phys. Rev. Lett., 110, 050402.

Details

Primary Language

English

Subjects

-

Journal Section

Research Article

Authors

Durgun Duran ^*
0000-0002-9458-3715
Türkiye

Publication Date

December 26, 2019

Submission Date

October 14, 2019

Acceptance Date

December 6, 2019

Published in Issue

Year 2019 Volume: 6 Number: 2

DOI

https://doi.org/10.35193/bseufbd.632771

IZ

https://izlik.org/JA47DX76XS

Cite

RIS / Bibtex

APA

Duran, D. (2019). Jaynes-Cummings Modelinde Çiftlenim Sabitinin Kuantum Tahmini. Bilecik Şeyh Edebali Üniversitesi Fen Bilimleri Dergisi, 6(2), 530-538. https://doi.org/10.35193/bseufbd.632771

AMA

1.Duran D. Jaynes-Cummings Modelinde Çiftlenim Sabitinin Kuantum Tahmini. Bilecik Şeyh Edebali Üniversitesi Fen Bilimleri Dergisi. 2019;6(2):530-538. doi:10.35193/bseufbd.632771

Chicago

Duran, Durgun. 2019. “Jaynes-Cummings Modelinde Çiftlenim Sabitinin Kuantum Tahmini”. Bilecik Şeyh Edebali Üniversitesi Fen Bilimleri Dergisi 6 (2): 530-38. https://doi.org/10.35193/bseufbd.632771.

EndNote

Duran D (December 1, 2019) Jaynes-Cummings Modelinde Çiftlenim Sabitinin Kuantum Tahmini. Bilecik Şeyh Edebali Üniversitesi Fen Bilimleri Dergisi 6 2 530–538.

IEEE

[1]D. Duran, “Jaynes-Cummings Modelinde Çiftlenim Sabitinin Kuantum Tahmini”, Bilecik Şeyh Edebali Üniversitesi Fen Bilimleri Dergisi, vol. 6, no. 2, pp. 530–538, Dec. 2019, doi: 10.35193/bseufbd.632771.

ISNAD

Duran, Durgun. “Jaynes-Cummings Modelinde Çiftlenim Sabitinin Kuantum Tahmini”. Bilecik Şeyh Edebali Üniversitesi Fen Bilimleri Dergisi 6/2 (December 1, 2019): 530-538. https://doi.org/10.35193/bseufbd.632771.

JAMA

1.Duran D. Jaynes-Cummings Modelinde Çiftlenim Sabitinin Kuantum Tahmini. Bilecik Şeyh Edebali Üniversitesi Fen Bilimleri Dergisi. 2019;6:530–538.

MLA

Duran, Durgun. “Jaynes-Cummings Modelinde Çiftlenim Sabitinin Kuantum Tahmini”. Bilecik Şeyh Edebali Üniversitesi Fen Bilimleri Dergisi, vol. 6, no. 2, Dec. 2019, pp. 530-8, doi:10.35193/bseufbd.632771.

Vancouver

1.Durgun Duran. Jaynes-Cummings Modelinde Çiftlenim Sabitinin Kuantum Tahmini. Bilecik Şeyh Edebali Üniversitesi Fen Bilimleri Dergisi. 2019 Dec. 1;6(2):530-8. doi:10.35193/bseufbd.632771