Skip to main content
Log in

Dynamics of quantum correlations under correlated noisy channels

  • Published:
Optical and Quantum Electronics Aims and scope Submit manuscript

Abstract

This study investigates the dynamical aspects of quantum correlations under two uses of noisy channels with memory. In this article, considering a family of pure entangled states, we study the quantum correlation in terms of entanglement and measurement-induced nonlocality (MIN) (based on trace distance and fidelity) when the consecutive actions of a quantum channel on the sequence of qubits have partial classical correlations. It is found that the quantum correlations monotonically decrease as the correlation strength increases, which indicates that the correlation measures strongly depend on both the noise parameter and the correlation strength of the channel. The results also illustrate that the memory effects offer more robustness against the considered noise. These findings give us insights into exploiting the resource content of the quantum state to achieve quantum advantages.

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

Similar content being viewed by others

Data availability

No data was used for the research described in the article.

References

  • Aaronson, B., Lo Franco, R., Adesso, G.: Comparative investigation of the freezing phenomena for quantum correlations under nondissipative decoherence. Phys. Rev. A 88, 012120 (2013)

    ADS  Google Scholar 

  • Addis, C., Karpa, G., Macchiavello, C., et al.: Dynamical memory effects in correlated quantum channels. Phys. Rev. A 94, 032121 (2016)

    ADS  Google Scholar 

  • Ahadpour, S., Mirmasoudi, F.: Dynamics of quantum correlations for different types of noisy channels. Opt. Quant. Electron. 52, 369 (2020)

    Google Scholar 

  • Banaszek, Konrad, Dragan, Andrzej, Wasilewski, Wojciech, Radzewicz, Czesław: Experimental demonstration of entanglement-enhanced classical communication over a quantum channel with correlated noise. Phys. Rev. Lett. 92, 257901 (2004)

    ADS  Google Scholar 

  • Bell, J.S.: On the Einstein-Podolsky-Rosen paradox. Physics 1, 195–200 (1964)

    MathSciNet  Google Scholar 

  • Biamonte, J., Wittek, P., Pancotti, N., Rebentrost, P., Wiebe, N., Lloyd, S.: Quantum machine learning. Nature 549, 195–202 (2017)

    Article  ADS  Google Scholar 

  • Dağ, C.B., Niedenzu, W., Ozaydin, F., Müstecaplıoğlu, Q.E., Kurizk, G.: Temperature control in dissipative cavities by entangled dimers. J. Phys. Chem. C 123, 4035–4043 (2019)

    Google Scholar 

  • Giovannetti, V., Lloyd, S., Maccone, L.: Quantum metrology. Phys. Rev. Lett. 96(1), 010401 (2006)

    ADS  MathSciNet  Google Scholar 

  • Goswami, S., Ghosh, S., Majumdar, A.S.: Protecting quantum correlations in presence of generalized amplitude damping channel: the two-qubit case. J. Phys. A: Math. Theor. 54, 045302 (2021)

    ADS  MATH  Google Scholar 

  • Guo, Y.-N., Fang, M.-F., Wang, G.-Y., Zeng, K.: Generation and protection of steady-state quantum correlations due to quantum channels with memory. Quant. Inf. Process. 15, 5129–5144 (2016)

    ADS  MathSciNet  MATH  Google Scholar 

  • Guo, Y.-N., Tian, Q.-L., Zeng, K., Li, Z.-D.: Quantum coherence of two-qubit over quantum channels with memory. Quant. Inf. Process. 16, 310 (2017)

    ADS  MathSciNet  MATH  Google Scholar 

  • Guo, Y.-N., Yang, C., Tian, Q.-L., Wang, G.-Y., Zeng, K.: Local quantum uncertainty and interferometric power for a two-qubit system under decoherence channels with memory. Quant. Inf. Process. 18, 375 (2019)

    ADS  MathSciNet  MATH  Google Scholar 

  • Guo, Y.-N., Zeng, K., Chen, P.-X.: Teleportation of quantum Fisher information under decoherence channels with memory. Laser Phys. Lett. 16, 095203 (2019)

    ADS  Google Scholar 

  • Guo, Y.-N., Tian, Q.-L., Zeng, K., Chen, P.-X.: Fidelity of quantum teleportation in correlated quantum channels. Quant. Inf. Process. 19, 182 (2020)

    ADS  MathSciNet  MATH  Google Scholar 

  • Horodecki, R., Horodecki, P., Horodecki, M., Horodecki, K.: Quantum entanglement. Rev. Mod. Phys. 81, 865 (2009)

    ADS  MathSciNet  MATH  Google Scholar 

  • Huang, Zhiming, Zhang, Cai: Protecting quantum correlation from correlated amplitude damping channel. Braz. J. Phys. 47, 400 (2017)

    ADS  Google Scholar 

  • Jozsa, R.: Fidelity for mixed quantum states. J. Mod. Opt. 41, 2315 (1994)

    ADS  MathSciNet  MATH  Google Scholar 

  • Kai, Xu., Zhang, Guo-Feng., Liu, Wu-Ming.: Quantum dynamical speedup in correlated noisy channels. Phys. Rev. A 100, 052305 (2019)

    ADS  Google Scholar 

  • Knill, E., Laflamme, R.: Power of one bit of quantum information. Phys. Rev. Lett. 81, 5672 (1998)

    ADS  Google Scholar 

  • Lo Franco, R., Compagno, G.: Quantum entanglement of identical particles by standard information-theoretic notions. Sci. Rep. 6, 1–10 (2016)

    Google Scholar 

  • Luo, S., Fu, S.: Measurement-induced nonlocality. Phys. Rev. Lett. 106, 120401 (2011)

    ADS  MATH  Google Scholar 

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

    ADS  Google Scholar 

  • Maziero, J., Celeri, L.C., Serra, R., Vedral, V.: Classical and quantum correlations under decoherence. Phys. Rev. A 80, 044102 (2009)

    ADS  MathSciNet  Google Scholar 

  • Ming-Liang, Hu., Fan, Heng: Measurement-induced nonlocality based on the trace norm. New J. Phys. 17, 033004 (2015)

    MATH  Google Scholar 

  • Mohamed, A.-B.A., Rahman, A.U., Eleuch, H.: Measurement uncertainty, purity, and entanglement dynamics of maximally entangled two qubits interacting spatially with isolated cavities: intrinsic decoherence effect. Entropy 24, 545 (2022)

    ADS  MathSciNet  Google Scholar 

  • Muthuganesan, R., Sankaranarayanan, R.: Fidelity based measurement induced nonlocality and its dynamics in quantum noisy channels. Phys. Lett. A 381, 3855–3859 (2017)

    ADS  MathSciNet  MATH  Google Scholar 

  • Muthuganesan, R., Sankaranarayanan, R.: Dynamics of measurement-induced nonlocality under decoherence. Quant. Inf. Process. 17, 305 (2018)

    ADS  MATH  Google Scholar 

  • Nielsen, M., Chuang, I.: Quantum computation and quantum information. Cambridge University Press, Cambridge (2010)

    MATH  Google Scholar 

  • Paladino, E., Faoro, L., Falci, G., Fazio, R.: Decoherence and 1/f Noise in Josephson Qubits. Phys. Rev. Lett. 88, 228304 (2002)

    ADS  Google Scholar 

  • Rahman, A.U., Khedif, Y., Javed, M., Ali, H., Daoud, M.: Characterizing two-qubit non-classical correlations and non-locality in mixed local dephasing noisy channels. Ann. Phys. 534, 2200197 (2022)

    MathSciNet  Google Scholar 

  • Rahman, A.U., Zidan, N., Zangi, S.M., Javed, M., Ali, H.: Quantum memory-assisted entropic uncertainty and entanglement dynamics: two qubits coupled with local fields and Ornstein Uhlenbeck noise. Quant. Inf. Process. 21, 354 (2022)

    ADS  MathSciNet  Google Scholar 

  • Rahman, A.U., Haddadi, S., Pourkarimi, M.R., Ghominejad, M.: Fidelity of quantum states in a correlated dephasing channel. Laser Phys. Lett. 19, 035204 (2022)

    ADS  Google Scholar 

  • Streltsov, A., Kampermann, H., Bruß, D.: Behavior of quantum correlations under Local Noise. Phys. Rev. Lett. 107, 170502 (2011)

    ADS  Google Scholar 

  • Suter, Dieter, Álvarez, Gonzalo A.: Protecting quantum information against environmental noise. Rev. Mod. Phys. 88, 041001 (2016)

    ADS  MathSciNet  Google Scholar 

  • Uola, R., Costa, Ana CS., Chau Nguyen, H., Gühne, O.: Quantum steering. Rev. Mod. Phys. 92, 015001 (2020)

    ADS  MathSciNet  Google Scholar 

  • Wang, Zhan-Yun., Qin, Zhi-Yong.: Quantum teleportation, entanglement, and Bell nonlocality in correlated noisy channels. Laser Phys. 30, 055201 (2020)

    ADS  Google Scholar 

  • Wang, X., Yu, C.-S., Yi, X.X.: An alternative quantum fidelity for mixed states of qudits. Phys. Lett. A 373, 58–60 (2008)

    ADS  MATH  Google Scholar 

  • Wang, Guo-you, Guo, You-neng, Deng, Zhihong: Dynamics of skew information-based quantum coherence under correlated noisy channels. J. Mod. Opt. 69, 531 (2022)

    ADS  MathSciNet  Google Scholar 

  • Werner, R.F.: Quantum states with Einstein-Podolsky-Rosen correlations admitting a hidden-variable model. Phys. Rev. A 40, 4277 (1989)

    ADS  MATH  Google Scholar 

  • Wootters, W.K.: Entanglement of Formation of an Arbitrary State of Two Qubits. Phys. Rev. Lett. 80, 2245 (1998)

    ADS  MATH  Google Scholar 

  • Yeo, Y., Skeen, A.: Time-correlated quantum amplitude-damping channel. Phys. Rev. A 67, 064301 (2003)

    ADS  Google Scholar 

  • Zhou, D., Joynt, R.: Phenomenological noise model for superconducting qubits: two-state fluctuators and 1/f noise. Sup. Sci. Tech. 25, 045003 (2012)

    ADS  Google Scholar 

  • Zurek, W.H.: Decoherence, einselection, and the quantum origins of the classical. Rev. Mod. Phys. 75, 715 (2003)

    ADS  MathSciNet  MATH  Google Scholar 

Download references

Acknowledgement

R.M. is grateful for the CTU Global Postdoc Fellowship Program and the financial support from M MT RVO 14000.

Funding

The authors have not disclosed any funding.

Author information

Authors and Affiliations

Authors

Contributions

MR, NA, RM and NS: Formulation, Manuscript Preparation. NA, RM: Writing and Editing.

Corresponding author

Correspondence to N. Ananth.

Ethics declarations

Conflict of interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Ethical approval

Not Applicable

Additional information

Publisher's Note

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

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

Rameshkumar, M., Ananth, N., Muthuganesan, R. et al. Dynamics of quantum correlations under correlated noisy channels. Opt Quant Electron 55, 732 (2023). https://doi.org/10.1007/s11082-023-05019-w

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s11082-023-05019-w

Keywords

Navigation