Skip to main content
SpringerLink
Log in

Relation between the roughness, linear entropy and visibility of a quantum state, the Jaynes–Cummings model

  • Published:
Journal of Computational Electronics Aims and scope Submit manuscript

Abstract

In this work, an analysis of the Jaynes–Cummings Model is conducted in the parameter spaces, composed of Roughness, Concurrence/Linear Entropy and Visibility. The analysis was carried out without including the effects of the environment and with the inclusion of a dispersive environment. As Roughness measures the state’s degree of non-classicality, its inclusion in the analysis allows to identify points in the dynamics that are not usually perceived by traditional analysis. It is observed that the parameter space is almost completely occupied when the dispersive term is small, and is concentrated in the region of less roughness and less purity as the dispersive coefficient is increased.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17
Fig. 18

Similar content being viewed by others

Availability of data and material

Not applicable.

Code availability

(software application or custom code) An open-source code QUTIP was used.

References

  1. Einstein, A.: Dtsch. Phys. Ges. Verh. 19, 82 (1917)

  2. Engel, A.: A Translation of the Paper Appears, the Collected Papers of Albert Einstein, vol. 6, Trans., Princeton U. Press, Princeton, NJ, 1997, p. 434

  3. Yin, J., Li, Y.H., Liao, S.K., et al.: Entanglement-based secure quantum cryptography over \(1,120\) kilometres. Nature 582, 501–505 (2020). https://doi.org/10.1038/s41586-020-2401-y

    Article  Google Scholar 

  4. Jacak, J.E., Jacak, W.A., Donderowicz, W.A., et al.: Quantum random number generators with entanglement for public randomness testing. Sci Rep 10, 164 (2020). https://doi.org/10.1038/s41567-019-0727-x

    Article  Google Scholar 

  5. Arute, F., Arya, K., Babbush, R., et al.: Quantum supremacy using a programmable superconducting processor. Nature 574, 505–510 (2019). https://doi.org/10.1038/s41586-019-1666-5

    Article  Google Scholar 

  6. Llewellyn, D., Ding, Y., Faruque, I.I., et al.: Chip-to-chip quantum teleportation and multi-photon entanglement in silicon. Nat. Phys. 16, 148–153 (2020). https://doi.org/10.1038/s41567-019-0727

    Article  Google Scholar 

  7. Brandão, F. G. S. L., Gour, G.: Reversible Framework for Quantum Resource Theories, Phys. Rev. Lett. 115, 070503 (2015); Phys. Rev. Lett. 115, 199901 (2015)

  8. Adesso, Gerardo, Bromley, Thomas R., Cianciaruso, Marco: Measures and applications of quantum correlations. J. Phys. A: Math. Theor. 49, 473001 (2016)

  9. Einstein, A., Podolsky, B., Rosen, N.: Can quantum-mechanical description of physical reality be considered complete? Phys. Rev. 47(10), 777–780 (1935)

    Article  Google Scholar 

  10. Bell, J.S.: On the impossible pilot wave”(PDF). Foundations of Physics. 12 (10): 989-99 (1982). Reprinted in Speakable and Unspeakable in Quantum Mechanics: Collected Papers on Quantum Philosophy. Cambridge University Press, p. 160 (2004)

  11. Omran, A., et al.: Generation and manipulation of Schrödinger cat states in Rydberg atom arrays. Science 365(6453), 570–574 (2019)

    Article  MathSciNet  Google Scholar 

  12. Gao, W.B., Lu, C.Y., Yao, X.C., et al.: Experimental demonstration of a hyper-entangled ten-qubit Schrödinger cat state. Nat. Phys. 6, 331–335 (2010)

    Article  Google Scholar 

  13. Leibfried, D., Knill, E., Seidelin, S., et al.: Creation of a six-atom“Schrödinger cat”state. Nature 438, 639–642 (2005)

  14. Zurek, W.H., Paz, J.P.: Decoherence, chaos, and the second law. Phys. Rev. Lett. 72, 2508 (1994)

    Article  Google Scholar 

  15. Oliveira, A.C., Nemes, M.C., Romero, K.M.: Fonseca. Phys Rev. E 68, 036214 (2003)

  16. Oliveira, A.C., Peixoto de Faria, J.G., Nemes, M.C.: Phys Rev. E 73, 046207 (2006)

  17. Wootters, William K.: Entanglement of formation of an arbitrary state of two qubits. Phys. Rev. Lett. 80, 2245–2248 (1998)

    Article  Google Scholar 

  18. Pranaw Rungta, Buz?ek, V., Caves, Carlton M., Hillery, M., Milburn, G. J.: Universal state inversion and concurrence in arbitrary dimensions. Phys Rev. A 64, 042315 (2001)

  19. Bosco-de-Magalhães, A.R., Adélcio, C.: Characteristic entanglement timescales of a qubit coupled to a quartic oscillator. Phys. Lett. A 380(4), 554–561 (2016)

    Article  Google Scholar 

  20. Magalhães, A. R, Bosco de., Oliveira, A. C.: Phys. Scr. 86 035001, (2012)

  21. Nemes, M.C., Furuya, K., Pellegrino, G.Q., Oliveira, A.C., Reis, M., Sanz, L.: Quantum entanglement and fixed point Hopf bifurcation. Phys. Lett. A V 354, 60–66 (2006)

    Article  MathSciNet  Google Scholar 

  22. Manfredi, G., Feix, M. R.: Phys. Rev. E 62, 4665, (2000)

  23. Kenfack, A., Zyczkowski, K.: Negativity of the Wigner function as an indicator of non-classicality, J. Opt. B, Quantum Semiclass. Opt. 6(10), 396 (2004)

  24. Lemos, H., Almeida, A., Amaral, B., Oliveira, A.: Roughness as classicality indicator of a quantum state. Phys. Lett. A 382(12), 823–836 (2018)

    Article  MathSciNet  Google Scholar 

  25. Luo, S., Zhang, Y.: Quantifying nonclassicality via Wigner-Yanase skew information. Phys. Rev. A, V. 100: 032116 (2019)

  26. Jaynes, E.T., Cummings, F.W.: Comparison of quantum and semiclassical radiation theories with application to the beam maser. Proc. IEEE 51(1) (1963)

  27. Gea-Banacloche, J.: 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)

    Article  Google Scholar 

  28. Gea-Banacloche, J.: Phys. Rev. A 44, 5913 (1991)

  29. Jakob, M., Bergou, J.A.: Quantitative complementarity relations in bipartite systems: entanglement as a physical reality. Opt. Commun. 283(5), 827–830 (2010)

    Article  Google Scholar 

  30. Schwaller, N., Dupertuis, M., Javerzac-Galy, C.: Evidence of the entanglement constraint on wave-particle duality using the IBM Q quantum computer. Phys. Rev. A 103, 022409 (2021)

  31. Loudon, R.: The Quantum Theory of Ligth. Oxford University Press, third edition (2000)

  32. Hamilton, C.S., Kruse, R., Sansoni, L., Barkhofen, S., Silberhorn, C., Jex, I.: Gaussian Boson sampling. Phys. Rev. Lett. 119, 170501 (2017). https://doi.org/10.1103/PhysRevLett.119.170501

  33. Quesada, N., Arrazola, J.M., Killoran, N.: Gaussian boson sampling using threshold detectors. Phys. Rev. A 98, 062322 (2018). https://doi.org/10.1103/PhysRevA.98.062322

  34. Zhong, H.-S., et al.: Quantum computational advantage using photons. Science (2020). https://doi.org/10.1126/science.abe8770

  35. Kowalewska-Kud-aszyk, A., Kalaga, J.K., Leoński, W.: Wigner-function nonclassicality as indicator of quantum chaos. Phys. Rev. E 78, 066219 (2008)

  36. Oliveira, A.C. Nemes, M.C.:Structures, Classical, in the Husimi distributions of stationary states for \(H_2\) and \(HCl\) molecules in the morse potential. Phys. Scr. 64, 279 (2001)

  37. Oliveira, A.C.: Semiclassical Husimi function of simple and chaotic systems. J. Modern Phys. 3(8), 694–701 (2012)

    Article  Google Scholar 

  38. Wunsche, A., Dodonov, V.V., Man’ko, O.V., Man’ko, V.I.: Fortschr. Phys. 49(10–11), 1117–1122 (2001)

  39. Ballentine, L.E.: The statistical interpretation of quantum mechanics. Rev. Mod. Phys. 42(4), 358 (1970)

    Article  Google Scholar 

  40. Ballentine, L.E., Yang, Y., Zibin, J.P.: Inadequacy of Ehrenfest’s theorem to characterize the classical regime. Phys. Rev. A 50(4), 2854 (1994)

    Article  Google Scholar 

  41. Ballentine, L.E., McRae, S.M.: Moment equations for probability distributions in classical and quantum mechanics. Phys. Rev. A 58(3), 1799 (1998)

    Article  Google Scholar 

  42. Ballentine, L.E.: Lyapunov exponents for the differences between quantum and classical dynamics. Phys. Rev. A 63(2), 024101 (2001)

  43. Wiebe, N., Ballentine, L. E.: Quantum mechanics of Hyperion. Phys. Rev. A, 72(2):022109 (2005)

  44. Reis, M., Oliveira, A. C.: Roughness as Entanglement Witness: The two Coupled Cavity Model 2018 SBFoton International Optics and Photonics Conference (SBFoton IOPC), Campinas, Brazil, pp. 1–5, (2018)

  45. Raimond, J.M., Brune, M., Haroche, S.: Rev. Mod. Phys. 73, 565 (2001)

  46. Arkhipov, I.I., Jan P., Jr., Jan, P., Adam, M.: Comparative study of nonclassicality, entanglement, and dimensionality of multimode noisy twin beams, Phys. Rev. A 91, 033837 (2015)

  47. Kalaga, J.K., Leoński, W.: Quantum steering borders in three-qubit systems. Quant. Inf. Process 16, 175 (2017)

    Article  Google Scholar 

  48. Kalaga, J. K., Leoński, W., Per̈ina, J.: Jr., Einstein-Podolsky-Rosen steering and coherence in the family of entangled three-qubit states, Phys. Rev. A 97, 042110 (2018)

  49. Oliveira, A.C., Magalhães A.R. Bosco de.: Phys. Rev. E 80, 026204 (2009)

  50. Davies, B. I., et al.: Visualizing spin degrees of freedom in atoms and molecules. Phys. Rev. A 100, 042102 (2019)

  51. Weinbub, J., Ferry, D.K.: Recent advances in Wigner function approaches. Appl. Phys. Rev. 5, 041104 (2018)

  52. Reis, M.., Oliveira, A.C.: Complementary Resource Relation of Concurrence and Roughness for a two Qubits State, arXiv:2106.00036

Download references

Funding

The authors gratefully acknowledge the support of the Brazilian Agency Fundação de Amparo à Pesquisa do Estado de Minas Gerais (FAPEMIG) through Grant No. APQ-01366-16.

Author information

Authors and Affiliations

  1. Departamento de Estatística, Física e Matemática, Universidade Federal de São João Del Rei, C.P. 131, Ouro Branco, MG, 36420 000, Brazil

    Mauricio Reis & Adélcio C. Oliveira

Authors
  1. Mauricio Reis
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Adélcio C. Oliveira
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

The work was equally divided by the authors.

Corresponding author

Correspondence to Adélcio C. Oliveira.

Ethics declarations

Conflict of interest

There is no conflict of interest.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Reis, M., Oliveira, A.C. Relation between the roughness, linear entropy and visibility of a quantum state, the Jaynes–Cummings model. J Comput Electron 20, 2189–2198 (2021). https://doi.org/10.1007/s10825-021-01761-0

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10825-021-01761-0

Keywords

Search

Navigation