Skip to main content
SpringerLink
Log in

Dynamics of classical and quantum correlations in a zigzag graphene nanoribbon under noisy environments

  • Published:
Quantum Information Processing Aims and scope Submit manuscript

Abstract

We study the dynamics of classical and quantum correlations between two edge spins in a zigzag graphene nanoribbon (ZGNR) under noisy channels including the bit flip, phase flip, and bit–phase flip channels. The results show that the classical correlation is insusceptible under these channels, which only depends on the spin correlation function. Quantum correlations including entanglement (E), discord (D), and dissonance (Q) in the ZGNR are robust against the thermal fluctuations and display the sudden death and birth behaviors, where the death region increases with increasing temperature. E only exists between the antiferromagnetically coupled two spins in the ZGNR. For the antiferromagnetically coupled states, Q exhibits the sudden change behaviors at the points where entanglement just appears and completely disappears. By comparison, we also find that C is always larger than E, but it is not always true that C > D in the ZGNR.

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

Similar content being viewed by others

References

  1. Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information. Cambridge University Press, Cambridge (2002)

    MATH  Google Scholar 

  2. Amico, L., Fazio, R., Osterloh, A., Vedral, V.: Entanglement in many-body systems. Rev. Mod. Phys. 80, 517 (2008)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  3. Bera, A., Das, T., Sadhukhan, D., Singha Roy, S., De Sen, A., Sen, U.: Quantum discord and its allies: a review of recent progress. Rep. Prog. Phys. 81, 024001 (2017)

    Article  ADS  MathSciNet  Google Scholar 

  4. 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 

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

    Article  ADS  MATH  Google Scholar 

  6. Tan, X.D., Huang, S.S., Jin, B.Q.: New insights into quantum and classical correlations in XY spin models. The Eur. Phys. J. B 85, 411 (2012)

    Article  ADS  MathSciNet  Google Scholar 

  7. Zhang, Y., He, Q., Hu, Z., Liu, J.: Quantum Dissonance as an Indicator of Quantum Phase Transition in the XXZ Chain. Chinese Phys. Lett. 31, 060302 (2014)

    Article  ADS  Google Scholar 

  8. Gardiner, C.W., Zoller, P.: Quantum Noise. Springer, Berlin (1991)

    Book  MATH  Google Scholar 

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

    Article  ADS  MathSciNet  Google Scholar 

  10. Xu, J., Xu, X., Li, C., Zhang, C., Zou, X., Guo, G.: Experimental investigation of classical and quantum correlations under decoherence. Nat. Commun. 1, 7 (2010)

    Article  ADS  Google Scholar 

  11. Bellomo, B., Lo Franco, R., Compagno, G.: Non-Markovian Effects on the Dynamics of Entanglement. Phys. Rev. Lett. 99, 160502 (2007)

    Article  ADS  Google Scholar 

  12. Fanchini, F.F., Werlang, T., Brasil, C.A., Arruda, L.G.E., Caldeira, A.O.: Non-Markovian dynamics of quantum discord. Phys. Rev. A 81, 052107 (2010)

    Article  ADS  Google Scholar 

  13. Aolita, L., de Melo, F., Davidovich, L.: Open-system dynamics of entanglement:a key issues review. Rep. Prog. Phys. 78, 042001 (2015)

    Article  ADS  Google Scholar 

  14. Mohammadi, H.: Post-Markovian dynamics of quantum correlations: entanglement versus discord. Quantum Inf. Process. 16, 39 (2016)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  15. Nourmandipour, A., Tavassoly, M.K., Rafiee, M.: Dynamics and protection of entanglement in n-qubit systems within Markovian and non-Markovian environments. Phys. Rev. A 93, 022327 (2016)

    Article  ADS  Google Scholar 

  16. Rangani Jahromi, H.: Relation between quantum probe and entanglement in n-qubit systems within Markovian and non-Markovian environments. J. Mod. Optic. 64, 1377 (2017)

    Article  ADS  Google Scholar 

  17. Gatto, D., De Pasquale, A., Giovannetti, V.: Degradation of entanglement in Markovian noise. Phys. Rev. A 99, 032307 (2019)

    Article  ADS  Google Scholar 

  18. Grimaudo, R., Isar, A., Mihaescu, T., Ghiu, I., Messina, A.: Dynamics of quantum discord of two coupled spin-1/2’s subjected to time-dependent magnetic fields. Results Phys. 13, 102147 (2019)

    Article  Google Scholar 

  19. Kuo, W., Akhtar, A.A., Arovas, D.P., You, Y.: Markovian entanglement dynamics under locally scrambled quantum evolution. Phys. Rev. B 101, 224202 (2020)

    Article  ADS  Google Scholar 

  20. Breuer, H.P., Laine, E.M., Piilo, J., Vacchini, B.: Non-Markovian dynamics in open quantum systems. Rev. Mod. Phys. 88, 021002 (2016)

    Article  ADS  Google Scholar 

  21. De Vega, I., Alonso, D.: Dynamics of non-Markovian open quantum systems. Rev. Mod. Phys. 89, 015001 (2017)

    Article  ADS  MathSciNet  Google Scholar 

  22. López, C.E., Romero, G., Lastra, F., Solano, E., Retamal, J.C.: Sudden birth versus sudden death of entanglement in multipartite systems. Phys. Rev. Lett. 101, 080503 (2008)

    Article  ADS  Google Scholar 

  23. Ficek, Z., Tanaś, R.: Delayed sudden birth of entanglement. Phys. Rev. A 77, 054301 (2008)

    Article  ADS  MATH  Google Scholar 

  24. Yu, T., Eberly, J.H.: Sudden death of entanglement. Science 323, 598 (2009)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  25. Deçordi, G. L., Vidiella-Barranco, A.: Sudden death of entanglement induced by a minimal thermal environment. Opt. Commun. 475, 126233 (2020)

  26. Sharma, K.K., Gerdt, V.P.: Entanglement sudden death and birth effects in two qubits maximally entangled mixed states under quantum channels. Int. J. Theor. Phys. 59, 403 (2020)

    Article  MathSciNet  MATH  Google Scholar 

  27. Almeida, M.P., Melo, F.D., Hor-Meyll, M., Salles, A., Walborn, S.P., Ribeiro, P., Davidovich, L.: Environment-induced sudden death of entanglement. Science 316, 579 (2007)

    Article  ADS  Google Scholar 

  28. Aguilar, G.H., Valdés-Hernández, A., Davidovich, L., Walborn, S.P., Souto Ribeiro, P.H.: Experimental entanglement redistribution under decoherence channels. Phys. Rev. Lett. 113, 240501 (2014)

    Article  ADS  Google Scholar 

  29. Wang, F., Hou, P.Y., Huang, Y.Y., Zhang, W.G., Ouyang, X.L., Wang, X., Huang, X.Z., Zhang, H.L., He, L., Chang, X.Y.: Observation of entanglement sudden death and rebirth by controlling solid-state spin bath. Phys. Rev. B 98, 064306 (2018)

    Article  ADS  Google Scholar 

  30. Krauter, H., Muschik, C.A., Jensen, K., Wasilewski, W., Petersen, J.M., Cirac, J.I., Polzik, E.S.: Entanglement generated by dissipation and steady state entanglement of two macroscopic objects. Phys. Rev. Lett. 107, 080503 (2011)

    Article  ADS  Google Scholar 

  31. Xu, J., Sun, K., Li, C., Xu, X., Guo, G., Andersson, E., Lo Franco, R., Compagno, G.: Experimental recovery of quantum correlations in absence of system-environment back-action. Nat. Commun. 4, 2851 (2013)

    Article  ADS  Google Scholar 

  32. Werlang, T., Souza, S., Fanchini, F.F., Villas Boas, C.J.: Robustness of quantum discord to sudden death. Phys. Rev. A 80, 024103 (2009)

    Article  ADS  Google Scholar 

  33. Loss, D., Divincenzo, D.P.: Quantum computation with quantum dots. Phys. Rev. A 57, 120 (1998)

    Article  ADS  Google Scholar 

  34. Novoselov, K.S., Geim, A.K., Morozov, S.V., Jiang, D., Zhang, Y., Dubonos, S.V., Grigorieva, I.V., Firsov, A.A.: Electric field effect in atomically thin carbon films. Science 306, 666 (2004)

    Article  ADS  Google Scholar 

  35. Burkard, G., Bulaev, D.V., Trauzettel, B., Loss, D.: Spin qubits in graphene quantum dots. Nat. Phys. 3, 192 (2007)

    Article  Google Scholar 

  36. Recher, P., Trauzettel, B.: Quantum dots and spin qubits in graphene. Nanotechnology 21, 302001 (2010)

    Article  Google Scholar 

  37. Giavaras, G., Nori, F.: Tunable quantum dots in monolayer graphene. Phys. Rev. B 85, 165446 (2012)

    Article  ADS  Google Scholar 

  38. Chen, C., Chang, Y.: Theoretical studies of graphene nanoribbon quantum dot qubits. Phys. Rev. B 92, 245406 (2015)

    Article  ADS  Google Scholar 

  39. Cimatti, I., Bondì, L., Serrano, G., Malavolti, L., Cortigiani, B., Velez-Fort, E., Betto, D., Ouerghi, A., Brookes, N.B., Loth, S., Mannini, M., Totti, F., Sessoli, R.: Vanadyl phthalocyanines on graphene/SiC(0001): toward a hybrid architecture for molecular spin qubits. Nanoscale Horiz. 4, 1202 (2019)

    Article  ADS  Google Scholar 

  40. Guo, G., Lin, Z., Tu, T., Cao, G., Li, X., Guo, G.: Quantum computation with graphene nanoribbon. New J. Phys. 11, 123005 (2009)

    Article  ADS  Google Scholar 

  41. Dragoman, D., Dragoman, M.: Graphene-based room-temperature implementation of a modified Deutsch-Jozsa quantum algorithm. Nanotechnology 26, 485201 (2015)

    Article  Google Scholar 

  42. Dragoman, D., Dragoman, M.: Quantum logic gates based on ballistic transport in graphene. J. Appl. Phys. 119, 094902 (2016)

    Article  ADS  Google Scholar 

  43. Dragoman, M., Dinescu, A., Dragoman, D.: Wafer-scale fabrication and room-temperature experiments on graphene-based gates for quantum computation. IEEE T. Nanotechnol. 17, 362 (2018)

    Article  ADS  Google Scholar 

  44. Deng, G., Wei, D., Li, S., Johansson, J.R., Kong, W., Li, H., Cao, G., Xiao, M., Guo, G., Nori, F., Jiang, H., Guo, G.: Coupling two distant double quantum dots with a microwave resonator. Nano Lett. 15, 6620 (2015)

    Article  ADS  Google Scholar 

  45. Deng, G., Wei, D., Johansson, J.R., Zhang, M., Li, S., Li, H., Cao, G., Xiao, M., Tu, T., Guo, G., Jiang, H., Nori, F., Guo, G.: Charge number dependence of the dephasing rates of a graphene double quantum dot in a circuit QED architecture. Phys. Rev. Lett. 115, 126804 (2015)

    Article  ADS  Google Scholar 

  46. Yazyev, O.V., Katsnelson, M.I.: Magnetic correlations at graphene edges: basis for novel spintronics devices. Phys. Rev. Lett. 100, 047209 (2008)

    Article  ADS  Google Scholar 

  47. Han, W., Kawakami, R.K., Gmitra, M., Fabian, J.: Graphene Spintronics. Nat. Nanotechnol. 9, 794 (2014)

    Article  ADS  Google Scholar 

  48. Golor, M., Wessel, S., Schmidt, M.J.: Quantum nature of edge magnetism in graphene. Phys. Rev. Lett. 112, 046601 (2014)

    Article  ADS  Google Scholar 

  49. Koop, C., Wessel, S.: Quantum phase transitions in effective spin-ladder models for graphene zigzag nanoribbons. Phys. Rev. B 96, 165114 (2017)

    Article  ADS  Google Scholar 

  50. Rhim, J., Moon, K.: Edge magnetism and quantum spin hall effect in zigzag graphene nanoribbon. Int. J. Mod. Phys. B 27, 1362011 (2013)

    Article  ADS  MathSciNet  Google Scholar 

  51. Pi, S., Dou, K., Tang, C., Kaun, C.: Site-dependent doping effects on quantum transport in zigzag graphene nanoribbons. Carbon 94, 196 (2015)

    Article  Google Scholar 

  52. Zhang, L.: Adiabatic quantum pump in a zigzag graphene nanoribbon junction. Chinese Phys. B 24, 117202 (2015)

    Article  ADS  Google Scholar 

  53. Grichuk, E.S., Manykin, E.A.: Spin polarized quantum pump effect in zigzag graphene nanoribbons. JETP Lett. 93, 372 (2011)

    Article  ADS  Google Scholar 

  54. Gräfe, M., Szameit, A.: Two-particle quantum correlations at graphene edges. 2D Mater. 2, 34005 (2015)

    Article  Google Scholar 

  55. Ruffieux, P., Wang, S., Yang, B., Sánchez-Sánchez, C., Liu, J., Dienel, T., Talirz, L., Shinde, P., Pignedoli, C.A., Passerone, D., Dumslaff, T., Feng, X., Müllen, K., Fasel, R.: On-surface synthesis of graphene nanoribbons with zigzag edge topology. Nature 531, 489 (2016)

    Article  ADS  Google Scholar 

  56. Kolmer, M., Steiner, A., Izydorczyk, I., Ko, W., Engelund, M., Szymonski, M., Li, A., Amsharov, K.: Rational synthesis of atomically precise graphene nanoribbons directly on metal oxide surfaces. Science 369, 571 (2020)

    Article  ADS  Google Scholar 

  57. Castro Neto, A.H., Guinea, F., Peres, N.M.R., Novoselov, K.S., Geim, A.K.: The electronic properties of graphene. Rev. Mod. Phys. 81, 109 (2009)

    Article  ADS  Google Scholar 

  58. Wakabayashi, K., Sasaki, K., Nakanishi, T., Enoki, T.: Electronic states of graphene nanoribbons and analytical solutions. Sci. Technol. Adv. Mat. 11, 054504 (2010)

    Article  Google Scholar 

  59. Koop, C., Schmidt, M.J.: Effective spin theories for edge magnetism in graphene zigzag ribbons. Phys. Rev. B 92, 125416 (2015)

    Article  ADS  Google Scholar 

  60. Koop, C.: Effective quantum spin models for graphene nanoribbons. PhD Thesis, RWTH Aachen University (2018).

  61. Aolita, L., de Melo, F., Davidovich, L.: Open-system dynamics of entanglement: a key issues review. Rep. Prog. Phys. 78, 042001 (2015)

    Article  ADS  Google Scholar 

  62. Yazyev, O.V.: Emergence of magnetism in graphene materials and nanostructures. Rep. Prog. Phys. 73, 056501 (2010)

    Article  ADS  Google Scholar 

  63. Ficek, Z., Tanaś, R.: Dark periods and revivals of entanglement in a two-qubit system. Phys. Rev. A 74, 024304 (2006)

    Article  ADS  Google Scholar 

Download references

Acknowledgements

We are grateful to Cornelie Koop for helpful discussions. This work was supported by the Natural Science Basic Research Program of Shaanxi (No. 2021JQ-837), National Natural Science Foundation of China (No. 11847042), Science and Technology Research Program of Shangluo University (No. 19SKY025), Innovation Team of Science and Technology Bureau in Shangluo (No. SK2017-46), and Natural Science Special Project of Shaanxi Provincial Department of Education (No. 17JK0236).

Author information

Author notes

  1. Xiao-Dong Tan and Le Zhang: These authors contributed equally to this work.

Authors and Affiliations

  1. School of Electronic Information and Electrical Engineering, Shangluo University, Shangluo, 726000, China

    Xiao-Dong Tan, Le Zhang, Xun-Feng Yuan & Shu-Ting Li

Authors
  1. Xiao-Dong Tan
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Le Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Xun-Feng Yuan
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Shu-Ting Li
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Xiao-Dong Tan.

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

Tan, XD., Zhang, L., Yuan, XF. et al. Dynamics of classical and quantum correlations in a zigzag graphene nanoribbon under noisy environments. Quantum Inf Process 21, 103 (2022). https://doi.org/10.1007/s11128-022-03439-3

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s11128-022-03439-3

Keywords

Search

Navigation