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Jaynes-Cummings Modelinde Çiftlenim Sabitinin Kuantum Tahmini

Year 2019, Volume: 6 Issue: 2, 530 - 538, 26.12.2019
https://doi.org/10.35193/bseufbd.632771

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. 

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.
Year 2019, Volume: 6 Issue: 2, 530 - 538, 26.12.2019
https://doi.org/10.35193/bseufbd.632771

Abstract

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.
There are 25 citations in total.

Details

Primary Language English
Journal Section Articles
Authors

Durgun Duran 0000-0002-9458-3715

Publication Date December 26, 2019
Submission Date October 14, 2019
Acceptance Date December 6, 2019
Published in Issue Year 2019 Volume: 6 Issue: 2

Cite

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