Skip to main content
SpringerLink
Log in

Local quantum uncertainty and interferometric power for a two-qubit system under decoherence channels with memory

  • Published:
Quantum Information Processing Aims and scope Submit manuscript

Abstract

Via local quantum uncertainty (LQU) and interferometric power (IP) as a measure of nonclassical correlations, we study the dynamics of quantum correlations for two non-interacting qubits passing through decoherence channels where the channels with successive uses are correlated. The effect of three different types of decoherence channels, such as amplitude damping, phase damping, and depolarizing channels, on quantum correlations has been discussed in detail. The explicit analytical expressions of LQU and IP for a class of Bell-diagonal states under these decoherence channels have been derived. Our results show that the behaviors of both LQU and IP exhibit similar variation under the amplitude damping and phase damping channels, with monotonic decay from an increasing decoherence rate, but decay more slowly when the memory coefficient of the channel increases. Compared to the phenomenon of LQU under a depolarizing channel, we find that there exists a sudden change of LQU under both amplitude damping and phase damping channels by choosing proper initial parameters. Finally, we compare the dynamics of LQU with that of IP under decoherence channels. Our results also confirm the amount of quantum correlations measured by LQU is smaller than IP.

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

Similar content being viewed by others

References

  1. Datta, A., Shaji, A., Caves, C.M.: Quantum discord and the power of one qubit. Phys. Rev. Lett. 100, 050502 (2008)

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  3. Devetak, I.: Distillation of local purity from quantum states. Phys. Rev. A 71, 062303 (2005)

    Article  ADS  Google Scholar 

  4. Rajagopal, A.K., Rendell, R.W.: Separability and correlations in composite states based on entropy methods. Phys. Rev. A 66, 022104 (2002)

    Article  ADS  MathSciNet  Google Scholar 

  5. Luo, S.: Using measurement-induced disturbance to characterize correlations as classical or quantum. Phys. Rev. A 77, 022301 (2008)

    Article  ADS  Google Scholar 

  6. Modi, K., Paterek, T., Son, W., Vedral, V., Williamson, M.: Unified view of quantum and classical correlations. Phys. Rev. Lett. 104, 080501 (2010)

    Article  ADS  MathSciNet  Google Scholar 

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

    Article  ADS  Google Scholar 

  8. Slaoui, A., Daoud, M., Ahl Laamara, R.: The dynamics of local quantum uncertainty and trace distance discord for two-qubit X states under decoherence: a comparative study. Quantum Inf. Process. 17, 178 (2018)

    Article  ADS  MathSciNet  Google Scholar 

  9. Slaoui, A., Shaukat, M.I., Daoud, M., Ahl Laamara, R.: Universal evolution of non-classical correlations due to collective spontaneous emission. Eur. Phys. J. Plus 133, 413 (2018)

    Article  Google Scholar 

  10. Sen, A., Sarkar, D., Bhar, A.: Local quantum uncertainty in two-qubit separable states: a case study. Quantum Inf. Process. 15, 233 (2016)

    Article  ADS  MathSciNet  Google Scholar 

  11. Khedif, Y., Daoud, M.: Local quantum uncertainty and trace distance discord dynamics for two-qubit X states embedded in non-Markovian environment. Int. J. Mod. Phys. B 32, 1850218 (2018)

    Article  ADS  MathSciNet  Google Scholar 

  12. Jebli, L., Benzimoune, B., Daoud, M.: Local quantum uncertainty for a class of two-qubit X states and quantum correlations dynamics under decoherence. Int. J. Quantum Inf. 15, 1750001 (2017)

    Article  Google Scholar 

  13. Jebli, L., Benzimoune, B., Daoud, M.: Quantum correlations for two-qubit X states through the local quantum uncertainty. Int. J. Quantum Inf. 15, 1750020 (2017)

    Article  MathSciNet  Google Scholar 

  14. Faizi, E., Ahansaz, B.: Local quantum uncertainty of SU(2) invariant states. J. Korean Phys. Soc. 67, 2033 (2015)

    Article  ADS  Google Scholar 

  15. Wang, S.H., Li, H., Lu, X., Long, G.L.: Closed form of local quantum uncertainty and a sudden change of quantum correlations. arXiv:1307.0576 (2013)

  16. Sales, J., Cardoso, W., Avelar, A., Almeida, N.: Dynamics of nonclassical correlations via local quantum uncertainty for atom and field interacting into a lossy cavity QED. Phys. A 443, 399 (2016)

    Article  MathSciNet  Google Scholar 

  17. Guo, J.L., Wei, J.L., Qin, W.: Examining quantum correlations in the XY spin chain by local quantum uncertainty. Quantum Inf. Process. 14, 1429 (2015)

    Article  ADS  Google Scholar 

  18. Habiballah, N., Khedif, Y., Daoud, M.: Local quantum uncertainty in XYZ Heisenberg spin models with Dzyaloshinski–Moriya interaction. Eur. Phys. J. D 72, 154 (2018)

    Article  ADS  Google Scholar 

  19. Slaoui, A., Bakmou, L., Daoud, M., Ahl Laamara, R.: A comparative study of local quantum Fisher information and local quantum uncertainty in Heisenberg XY model. Phys. Lett. A 383, 2241 (2019)

    Article  ADS  MathSciNet  Google Scholar 

  20. Coulamy, I.B., Warnes, J.H., Sarandy, M.S., Saguia, A.: Scaling of the local quantum uncertainty at quantum phase transitions. Phys. Lett. A 380, 1724 (2016)

    Article  ADS  MathSciNet  Google Scholar 

  21. Carrijo, T.M., Avelar, A.T., Celeri, L.C.: Quantum uncertainty in critical systems with three spins interaction. J. Phys. B At. Mol. Opt. Phys. 48, 125501 (2015)

    Article  ADS  Google Scholar 

  22. He, Z., Yao, C., Wang, Q., Zou, J.: Measuring non-Markovianity based on local quantum uncertainty. Phys. Rev. A 90, 042101 (2014)

    Article  ADS  Google Scholar 

  23. Wu, S., Zhang, Y., Yu, C.: Local quantum uncertainty guarantees the measurement precision for two coupled two-level systems in non-Markovian environment. Ann. Phys. 390, 71 (2018)

    Article  ADS  MathSciNet  Google Scholar 

  24. Yu, C.S., Wu, S.X., Wang, X., Yi, X.X., Song, H.S.: Quantum correlation measure in arbitrary bipartite systems. Eur. Phys. Lett. 107, 10007 (2014)

    Article  ADS  Google Scholar 

  25. Girolami, D., Souza, A.M., Giovannetti, V., Tufarelli, T., Filgueiras, J.G., Sarthour, R.S., Soares-Pinto, D.O., Oliveira, I.S., Adesso, G.: Quantum discord determines the interferometric power of quantum states. Phys. Rev. Lett. 112, 210401 (2014)

    Article  ADS  Google Scholar 

  26. Kim, S., Li, L., Kumar, A., Wu, J.: Characterizing nonclassical correlations via local quantum Fisher information. Phys. Rev. A 97, 032326 (2018)

    Article  ADS  MathSciNet  Google Scholar 

  27. Luo, S.: Wigner–Yanase skew information versus quantum Fisher information. Proc. Am. Math. Soc. 132, 885 (2003)

    Article  Google Scholar 

  28. Bera, M.N.: Role of quantum correlation in metrology beyond standard quantum limit. arXiv:1405.5357 (2014)

  29. Braunstein, S.L., Caves, C.M.: Statistical distance and the geometry of quantum states. Phys. Rev. Lett. 72, 3439 (1994)

    Article  ADS  MathSciNet  Google Scholar 

  30. Macchiavello, C., Massimo Palma, G.: Entanglement-enhanced information transmission over a quantum channel with correlated noise. Phys. Rev. A 65, 050301 (2002)

    Article  ADS  Google Scholar 

  31. Yeo, Y., Skeen, A.: Time-correlated quantum amplitudedamping channel. Phys. Rev. A 67, 064301 (2003)

    Article  ADS  Google Scholar 

  32. D’Arrigo, A., Benenti, G., Falci, G.: Quantum capacity of dephasing channels with memory. New J. Phys. 9, 310 (2007)

    Article  ADS  Google Scholar 

  33. Macchiavello, C., Palma, G.M., Virmani, S.: Transition behavior in the channel capacity of two-quibit channels with memory. Phys. Rev. A 69, 010303 (2004)

    Article  ADS  Google Scholar 

  34. Arshed, N., Toor, A.: Entanglement-assisted classical capacity of quantum channels with correlated noise. Phys. Rev. A 73, 014304 (2006)

    Article  ADS  Google Scholar 

  35. Wolf, M., García, D.: Quantum capacities of channels with small environment. Phys. Rev. A 75, 012303 (2007)

    Article  ADS  Google Scholar 

  36. Benenti, G., D’Arrigo, A., Falci, G.: Enhancement of transmission rates in quantum memory channels with damping. Phys. Rev. Lett. 103, 020502 (2009)

    Article  ADS  Google Scholar 

  37. D’Arrigo, A., Benenti, G., Falci, G.: Transmission of classical and quantum information through a quantum memory channel with damping. Eur. Phys. J. D 66, 66 (2012)

    Article  Google Scholar 

  38. Leung, D., Watrous, J.: On the complementary quantum capacity of the depolarizing channel. Quantum 1, 28 (2017)

    Article  Google Scholar 

  39. Hu, M.L., Fan, H.: Quantum coherence of multiqubit states in correlated noisy channels. arXiv:1812.04385 (2018)

Download references

Acknowledgements

This work is supported by the National Natural Science Foundation of China under Grant No. 11747107, the Natural Science Foundation of Hunan Province (Grant No. 2017JJ3346), the Project of Science and Technology Plan of Changsha (K1705022 and kc1809023), the Scientific Research Project of Hunan Province Department of Education (Grant No. 18A373) and Key Laboratory of Low-Dimensional Quantum Structures and Quantum Control of Ministry of Education (QSQC1810).

Author information

Authors and Affiliations

  1. College of Electronic Communication and Electrical Engineering, Changsha University, Changsha, 410022, Hunan, People’s Republic of China

    You-neng Guo, Cheng Yang & Ke Zeng

  2. College of Mathematics and Computing Science, Changsha University, Changsha, 410022, Hunan, People’s Republic of China

    Qing-long Tian

  3. College of Science, Hunan University of Technology, Zhuzhou, 412007, Hunan, China

    Guo-you Wang

Authors
  1. You-neng Guo
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Cheng Yang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Qing-long Tian
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Guo-you Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Ke Zeng
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to You-neng Guo.

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

Guo, Yn., Yang, C., Tian, Ql. et al. Local quantum uncertainty and interferometric power for a two-qubit system under decoherence channels with memory. Quantum Inf Process 18, 375 (2019). https://doi.org/10.1007/s11128-019-2490-4

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s11128-019-2490-4

Keywords

Search

Navigation