Skip to main content
Log in

Quantum Fisher information versus quantum skew information in double quantum dots with Rashba interaction

  • Research
  • Published:
Applied Physics B Aims and scope Submit manuscript

Abstract

Exploring the basic features of solid-state systems is a crucial route for reaping their quantum advantages. Quantum dots (QDs) emerge as a flexible substrate for technical advances in computing power and nanodevices. In this regard, a proposed model to inspect the behavior of thermal correlations in terms of local quantum Fisher information and local quantum uncertainty in double QDs with the interplay of Rashba spin–orbit interaction is examined. The Rashba spin–orbit interaction is externally adjustable and can be used to tune the quantum correlations present in the system. Consequently, we show that the dynamics of logarithmic negativity, skew information, and local quantum Fisher information change in terms of the Rashba coupling, the double QDs’ parameters, and temperature. Importantly, we also demonstrate that we can tweak specific parameters to preserve quantum resources in the system. These observations give a solid grasp of the quantum features of such a quantum dot system, showing promise for establishing quantum technologies.

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

Access this article

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

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8

Similar content being viewed by others

Data availability statement

This research is a theoretical work and has no associated data.

References

  1. C.H. Bennett, G. Brassard, C. Crépeau, R. Jozsa, A. Peres, W.K. Wootters, Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels. Phys. Rev. Lett. 70(13), 1895–1899 (1993)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  2. K. El Anouz, A. El Allati, N. Metwally, Teleportation two-qubit state by using two different protocols. Opt. Quant. Electron. 51(6), 1–16 (2019)

    Article  Google Scholar 

  3. M. Mansour, Z. Dahbi, Quantum secret sharing protocol using maximally entangled multi-qudit states. Int. J. Theor. Phys. 59(12), 3876–3887 (2020)

    Article  MathSciNet  MATH  Google Scholar 

  4. K. El Anouz, A. El Allati, F. Saif, Study different quantum teleportation amounts by solving Lindblad master equation. Phys. Scr. 97(3), 035102 (2022)

    Article  ADS  Google Scholar 

  5. K.E. Artur, Quantum Cryptography and Bell’s Theorem. In Quantum Measurements in Optics, pages 413–418. Springer US, (1992)

  6. A. El Allati, H. Amellal, N. Metwally, S. Aliloute, Entanglement and quantum teleportation via dissipative cavities. Opt. Laser Technol. 116, 13–17 (2019)

    Article  ADS  Google Scholar 

  7. H. Michal, H. Pawel, H. Ryszard, On the necessary and sufficient conditions for separability of mixed quantum states. (1996) arXiv preprint quant-ph/9605038

  8. W.K. Wootters, Entanglement of Formation of an Arbitrary State of Two Qubits. Phys. Rev. Lett. 80(10), 2245–2248 (1998)

    Article  ADS  MATH  Google Scholar 

  9. G. Vidal, R.F. Werner, Computable measure of entanglement. Phys. Rev. A 65(3), 032314 (2002)

    Article  ADS  Google Scholar 

  10. M.B. Plenio, Logarithmic negativity: a full entanglement monotone that is not convex. Phys. Rev. Lett. 95(9), 090503 (2005)

    Article  ADS  MathSciNet  Google Scholar 

  11. M. Mansour, Z. Dahbi, Entanglement of bipartite partly non-orthogonal \(\frac{1}{2}\)-spin coherent states. Laser Phys. 30(8), 085201 (2020)

    Article  ADS  Google Scholar 

  12. M. Mansour, Z. Dahbi, M. Essakhi, A. Salah, Quantum correlations through spin coherent states. Int. J. Theor. Phys. 60(6), 2156–2174 (2021)

    Article  MathSciNet  MATH  Google Scholar 

  13. H. Ollivier, W.H. Zurek, Quantum discord: a measure of the quantumness of correlations. Phys. Rev. Lett. 88(1), 017901 (2001)

    Article  ADS  MATH  Google Scholar 

  14. M.H. Ali Saif, L. Behzad, S.J. Pramod, Tight lower bound to the geometric measure of quantum discord. Phys. Rev. A, 85(2), February (2012)

  15. F. Ciccarello, T. Tufarelli, V. Giovannetti, Toward computability of trace distance discord. New J. Phys. 16(1), 013038 (2014)

    Article  ADS  MATH  Google Scholar 

  16. D. Girolami, T. Tufarelli, G. Adesso, Characterizing nonclassical correlations via local quantum uncertainty. Phys. Rev. Lett. 110(24), 240402 (2013)

    Article  ADS  Google Scholar 

  17. E.P. Wigner, M.M. Yanase, Information contents of distributions. Proc. Natl. Acad. Sci. 49(6), 910–918 (1963)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  18. B. Ye, Z. Zhang, Quantum correlated coherence and Hellinger distance in the critical systems. Mod. Phys. Lett. A 36(02), 2150002 (2020)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  19. A. Sbiri, M. Mansour, Y. Oulouda, Local quantum uncertainty versus negativity through Gisin states. Int. J. Quantum Inf. 19(05), 2150023 (2021)

    Article  MathSciNet  MATH  Google Scholar 

  20. A. Sbiri, M. Oumennana, M. Mansour, Thermal quantum correlations in a two-qubit Heisenberg model under Calogero-Moser and Dzyaloshinsky-Moriya interactions. Mod. Phys. Lett. B 36(09), 2150618 (2022)

    Article  ADS  MathSciNet  Google Scholar 

  21. C. Yang, Y.-N. Guo, H.-P. Peng, L. Yi-Bing, Dynamics of local quantum uncertainty for a two-qubit system under dephasing noise. P. Soc. Photo-opt. Ins. 30(1), 015203 (2019)

    Google Scholar 

  22. M. Essakhi, Y. Khedif, M. Mansour, M. Daoud, Intrinsic decoherence effects on quantum correlations dynamics. Opt. Quantum Electron. 54(2), 1–15 (2022)

    Article  Google Scholar 

  23. S. Elghaayda, Z. Dahbi, M. Mansour, Local quantum uncertainty and local quantum Fisher information in two-coupled double quantum dots. Opt. Quantum Electron. 54(7), 1–15 (2022)

    Article  Google Scholar 

  24. E. Chaouki, Z. Dahbi, M. Mansour, Dynamics of quantum correlations in a quantum dot system with intrinsic decoherence effects. Int. J. Mod. Phys. B, p. 2250141, (2022)

  25. S. Kim, L. Li, A. Kumar, W. Junde, Characterizing nonclassical correlations via local quantum Fisher information. Phys. Rev. A 97(3), 032326 (2018)

    Article  ADS  MathSciNet  Google Scholar 

  26. K. El Anouz, A. El Allati, Teleporting quantum Fisher information under Davies-Markovian dynamics. Phys. A 596, 127133 (2022)

    Article  MathSciNet  MATH  Google Scholar 

  27. K. El Anouz, A. El Allati, N. Metwally, T. Mourabit, Estimating the teleported initial parameters of a single- and two-qubit systems. Appl. Phys. B 125(1), 1–15 (2018)

    Google Scholar 

  28. K. El Anouz, A. El Allati, A. Salah, F. Saif, Quantum fisher information: probe to measure fractional evolution. Int. J. Theor. Phys. 59(5), 1460–1474 (2020)

    Article  MathSciNet  MATH  Google Scholar 

  29. A. Mark, Reed. Quantum Dots. Sci. Am. 268(1), 118–123 (1993)

    Google Scholar 

  30. D. Loss, D.P. DiVincenzo, Quantum computation with quantum dots. Phys. Rev. A 57(1), 120–126 (1998)

    Article  ADS  Google Scholar 

  31. J.R. Petta, A.C. Johnson, J.M. Taylor, E.A. Laird, A. Yacoby, M.D. Lukin, C.M. Marcus, M.P. Hanson, A.C. Gossard, Coherent manipulation of coupled electron spins in semiconductor quantum dots. Science 309(5744), 2180–2184 (2005)

    Article  ADS  Google Scholar 

  32. F. Bodoky, W. Belzig, C. Bruder, Connection between noise and quantum correlations in a double quantum dot. Phys. Rev. B 77(3), 035302 (2008)

    Article  ADS  Google Scholar 

  33. H.A. Mansour, F.-Z. Siyouri, M. Faqir, M.E. Baz, Quantum correlations dynamics in two coupled semiconductor InAs quantum dots. Phys. Scr. 95(9), 095101 (2020)

    Article  ADS  Google Scholar 

  34. V. Galitski, I.B. Spielman, Spin-orbit coupling in quantum gases. Nature 494(7435), 49–54 (2013)

    Article  ADS  Google Scholar 

  35. X. Wen, Y. Guo, Rashba and Dresselhaus spin-orbit coupling effects on tunnelling through two-dimensional magnetic quantum systems. Phys. Lett. A 340(1–4), 281–289 (2005)

    ADS  Google Scholar 

  36. G. Dresselhaus, Spin-orbit coupling effects in zinc blende structures. Phys. Rev. 100(2), 580–586 (1955)

    Article  ADS  MATH  Google Scholar 

  37. Y.A. Bychkov, É.I. Rashba, Properties of a 2D electron gas with lifted spectral degeneracy. JETP Lett. 39(2), 78 (1984)

    ADS  Google Scholar 

  38. Y.A. Bychkov, E.I. Rashba, Oscillatory effects and the magnetic susceptibility of carriers in inversion layers. J. Phys. C Solid State Phys. 17(33), 6039–6045 (1984)

    Article  ADS  Google Scholar 

  39. M. Ferreira, O. Rojas, M. Rojas. Thermal entanglement and quantum coherence of a single electron in a double quantum dot with Rashba Interaction. arXiv preprint arXiv:2203.06301, (2022)

  40. T. Chakraborty, P. Pietiläinen, Electron correlations in a quantum dot with Bychkov-Rashba coupling. Phys. Rev. B 71(11), 113305 (2005)

    Article  ADS  Google Scholar 

  41. E. Tsitsishvili, G.S. Lozano, A.O. Gogolin, Rashba coupling in quantum dots: an exact solution. Phys. Rev. B 70(11), 115316 (2004)

    Article  ADS  Google Scholar 

  42. V. Vedral, The role of relative entropy in quantum information theory. Rev. Mod. Phys. 74(1), 197–234 (2002)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  43. C.W. Helstrom, Quantum detection and estimation theory. J. Stat. Phys. 1(2), 231–252 (1969)

    Article  ADS  MathSciNet  Google Scholar 

  44. M.G. Genoni, S. Olivares, M.G.A. Paris, Optical phase estimation in the presence of phase diffusion. Phys. Rev. Lett. 106(15), 153603 (2011)

    Article  ADS  Google Scholar 

  45. F. Chapeau-Blondeau, Entanglement-assisted quantum parameter estimation from a noisy qubit pair: a Fisher information analysis. Phys. Lett. A 381(16), 1369–1378 (2017)

    Article  ADS  MathSciNet  Google Scholar 

  46. V. Giovannetti, S. Lloyd, L. Maccone, Quantum-enhanced measurements: beating the standard quantum limit. Science 306(5700), 1330–1336 (2004)

    Article  ADS  Google Scholar 

  47. S.F. Huelga, C. Macchiavello, T. Pellizzari, A.K. Ekert, M.B. Plenio, J.I. Cirac, Improvement of frequency standards with quantum entanglement. Phys. Rev. Lett. 79(20), 3865–3868 (1997)

    Article  ADS  Google Scholar 

  48. F. Chapeau-Blondeau, Optimizing qubit phase estimation. Phys. Rev. A 94(2), 022334 (2016)

    Article  ADS  Google Scholar 

  49. B.-L. Ye, B. Li, Z.-X. Wang, X. Li-Jost, S.-M. Fei, Quantum Fisher information and coherence in one-dimensional XY spin models with Dzyaloshinsky-Moriya interactions. Sci. China Phys. Mech. Astron. 61(11), 1–7 (2018)

    Article  Google Scholar 

  50. M.G.A. Paris, Quantum estimation for quantum technology. Int. J. Quantum Inf. 7(1), 125–137 (2009)

    Article  MATH  Google Scholar 

  51. G. Karpat, B. Çakmak, F.F. Fanchini, Quantum coherence and uncertainty in the anisotropic XY chain. Phys. Rev. B 90(10), 104431 (2014)

    Article  ADS  Google Scholar 

  52. J.-L. Guo, J.-L. Wei, W. Qin, M. Qing-Xia, Examining quantum correlations in the XY spin chain by local quantum uncertainty. Quantum Inf. Process. 14(4), 1429–1442 (2015)

    Article  ADS  MATH  Google Scholar 

  53. S. Luo, Wigner-Yanase skew information vs. quantum Fisher information. Proc. Am. Math. Soc. 132(3), 885–890 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  54. S. Luo, Wigner-Yanase skew information and uncertainty relations. Phys. Rev. Lett. 91(18), 180403 (2003)

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Contributions

MM conceived of the presented idea. ZD; KE and MO performed the analytic calculations and graphical tasks. All authors have contributed to interpreting the results. All authors have contributed to writing the manuscript. All authors have read and agreed to the final version of the manuscript.

Corresponding author

Correspondence to M. Mansour.

Ethics declarations

Conflict of interest

All the authors state that they have no identified competing financial interests that could have arisen to impact this research.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Dahbi, Z., Oumennana, M., Anouz, K.E. et al. Quantum Fisher information versus quantum skew information in double quantum dots with Rashba interaction. Appl. Phys. B 129, 27 (2023). https://doi.org/10.1007/s00340-022-07963-z

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s00340-022-07963-z

Navigation