Skip to main content
SpringerLink
Log in

Three-qubit entanglement generation of quantum states dissipating into a common environment

  • Published:
Quantum Information Processing Aims and scope Submit manuscript

Abstract

In this paper, we investigate the dynamics of entanglement of three-qubit states of a system dissipating into a common environment. By using the tripartite negativity as entanglement measure, our results imply that the three-qubit entanglement can be generated among the three qubits which have no interaction with each other, but interact with the common environment independently. From our analysis, we find that the three-qubit entanglement increases from zero to a stable value which varies with the size of the system with the increasing of the scaled time. Additionally, the extension of the entanglement generation to an arbitrary size of a subsystem is made and some discussion is given.

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

Similar content being viewed by others

References

  1. Bennett, C.H.: Quantum cryptography using any two nonorthogonal states. Phys. Rev. Lett. 68, 3121 (1992)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  2. Bennett, C.H., Wiesner, S.J.: Communication via one- and two-particle operators on Einstein–Podolsky–Rosen states. Phys. Rev. Lett. 69, 2881 (1992)

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

  4. Peres, A.: Separability criterion for density matrices. Phys. Rev. Lett. 77, 1413 (1996)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  5. Wootters, W.K.: Entanglement of formation of an arbitrary state of two qubits. Phys. Rev. Lett. 80, 2245 (1998)

    Article  ADS  Google Scholar 

  6. Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information, Chap. 3. Cambridge University Press, Cambridge (2000)

    MATH  Google Scholar 

  7. Gisin, N., Ribordy, G., Tittel, W., Zbinden, H.: Quantum cryptography. Rev. Mod. Phys. 74, 145 (2002)

    Article  ADS  Google Scholar 

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

    Article  MathSciNet  ADS  MATH  Google Scholar 

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

    Article  MathSciNet  ADS  MATH  Google Scholar 

  10. Eisert, J., Cramer, M., Plenio, M.B.: Colloquium: area laws for the entanglement entropy. Rev. Mod. Phys. 82, 277 (2010)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  11. Modi, K., Brodutch, A., Cable, H., Paterek, T., Vedral, V.: The classical-quantum boundary for correlations: discord and related measures. Rev. Mod. Phys. 84, 1655 (2012)

    Article  ADS  Google Scholar 

  12. Pan, J.-W., Chen, Z.-B., Weinfurter, H., Zeilinger, A.: Zukowski, : Multiphoton entanglement and interferometry. Rev. Mod. Phys. 84, 777 (2012)

    Article  ADS  Google Scholar 

  13. Silva, I.A., Girolami, D., Auccaise, R., Sarthour, R.S., Oliveira, I.S., Bonagamba, T.J., deAzevedo, E.R., Soares-Pinto, D.O., Adesso, G.: Measuring bipartite quantum correlations of an unknown state. Phys. Rev. Lett. 110, 140501 (2013)

    Article  ADS  Google Scholar 

  14. Zyczkowski, K., Horodecki, P., Sanpera, A., Lewenstein, M.: Volume of the set of separable states. Phys. Rev. A 58, 883 (1998)

    Article  MathSciNet  ADS  Google Scholar 

  15. Vidal, G., Werner, R.F.: A computable measure of entanglement. Phys. Rev. A 65, 032314 (2002)

    Article  ADS  Google Scholar 

  16. Hiroshima, T., Adesso, G., Illuminati, F.: Monogamy inequality for distributed Gaussian entanglement. Phys. Rev. Lett. 98, 050503 (2007)

    Article  ADS  Google Scholar 

  17. Devi, Usha: A.R., Prabhu, R., Rajagopal, A.K.: Characterizing multiparticle entanglement in symmetric N-qubit states via negativity of covariance matrices. Phys. Rev. Lett. 98, 060501 (2007)

    Article  ADS  Google Scholar 

  18. Rodo, C., Adesso, G., Sanpera, A.: Quantum information with continuous variable systems. Phsy. Rev. Lett. 100, 110505 (2008)

    Article  ADS  Google Scholar 

  19. Calabrese, P., Cardy, J., Tonni, E.: Entanglement negativity in quantum field theory. Phsy. Rev. Lett. 109, 130502 (2012)

    Article  ADS  Google Scholar 

  20. Kreis, K., van Loock, P.: Classifying, quantifying, and witnessing qudit-qumode hybrid entanglement. Phys. Rev. A 85, 032307 (2012)

    Article  ADS  Google Scholar 

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

    Article  MathSciNet  ADS  MATH  Google Scholar 

  22. Sadiek, G., Alkurtass, B., Aldossary, O.: Entanglement in a time-dependent coupled XY spin chain in an external magnetic field. Phy. Rev. A 82, 052337 (2010)

    Article  ADS  Google Scholar 

  23. Rudner, M.S., Vandersypen, L.M.K., Vuleti, V., Levitov, L.S.: Generating entanglement and squeezed states of nuclear spins in quantum dots. Phsy. Rev. Lett. 107, 206806 (2011)

    Article  ADS  Google Scholar 

  24. Chin, A.W., Huelga, S.F., Plenio, M.B.: Quantum metrology in non-Markovian environments. Phys. Rev. Lett. 109, 233601 (2012)

    Article  ADS  Google Scholar 

  25. Qin, W., Wang, C., Long, G.L.: High-dimensional quantum state transfer through a quantum spin chain. Phys. Rev. A 87, 012339 (2013)

    Article  ADS  Google Scholar 

  26. Zippilli, S., Paternostro, M., Adesso, G., Illuminati, F.: Entanglement replication in driven dissipative many-body systems. Phys. Rev. Lett. 110, 040503 (2013)

    Article  ADS  Google Scholar 

  27. Plenio, M.B., Huelga, S.F.: Entangled light from white noise. Phys. Rev. Lett. 88, 197901 (2002)

    Article  ADS  Google Scholar 

  28. Clark, S., Peng, A., Gu, M., Parkins, S.: ibid. 91, 177901 (2003)

  29. Mancini, S., Wang, J.: Towards feedback control of entanglement. Eur. Phys. J. D 32, 257 (2005)

    Article  ADS  Google Scholar 

  30. Hartmann, L., Dur, W., Briegel, H.J.: Steady-state entanglement in open and noisy quantum systems. Phys. Rev. A 74, 052304 (2006)

    Article  ADS  Google Scholar 

  31. Angelakis, D., Bose, S., Mancini, S.: Steady-state entanglement between hybrid light-matter qubits. Europhys. Lett. 85, 20007 (2009)

    Google Scholar 

  32. 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 

  33. Ghosh, B., Majumdar, A.S., Nayak, N.: Environment-assisted entanglement enhancement. Phys. Rev. A 74, 052315 (2006)

    Article  ADS  Google Scholar 

  34. Memarzadeh, L., Mancini, S.: Stationary entanglement achievable by environment-induced chain links. Phys. Rev. A 83, 042329 (2011)

    Article  ADS  Google Scholar 

  35. Rafiee, M., Lupo, C., Mokhtari, H., Mancini, S.: Stationary and uniform entanglement distribution in qubit networks with quasilocal dissipation. Phys. Rev. A 85, 042320 (2012)

    Article  ADS  Google Scholar 

  36. Huelga, S.F., Rivas, A., Plenio, M.B.: Non-Markovianity-assisted steady state entanglement. Phys. Rev. Lett. 108, 160402 (2012)

    Article  ADS  Google Scholar 

  37. Braun, D.: Creation of entanglement by interaction with a common heat bath. Phys. Rev. Lett. 89, 277901 (2002)

    Article  ADS  Google Scholar 

  38. Benatti, F., Floreanini, R., Piani, M.: Environment induced entanglement in Markovian dissipative dynamics. Phys. Rev. Lett. 91, 070402 (2003)

    Article  ADS  Google Scholar 

  39. Memarzadeh, L., Mancini, S.: Entanglement dynamics for qubits dissipating into a common environment. Phys. Rev. A 87, 032303 (2013)

    Article  ADS  Google Scholar 

  40. Lu, H.-Z., Zhao, J.-Q., Cao, L.-Z., Wang, X.-Q.: Experimental investigation of the robustness against noise for different Bell-type inequalities in three-qubit Greenberger–Horne–Zeilinger states. Phys. Rev. A 84, 044101 (2011)

  41. Giorgi, G.L.: Monogamy properties of quantum and classical correlations. Phys. Rev. A 84, 054301 (2011)

    Article  ADS  Google Scholar 

  42. Eltschka, C., Siewert, J.: Entanglement of three-qubit Greenberger–Horne–Zeilinger-symmetric states. Phys. Rev. Lett. 108, 020502 (2012)

  43. Laskowski, W., Richart, D., Schwemmer, C., Paterek, T., Weinfurter, H.: Experimental Schmidt decomposition and state independent entanglement detection. Phys. Rev. Lett. 108, 240501 (2012)

    Article  ADS  Google Scholar 

  44. Zhao, M.-J., Zhang, T.-G., Li-Jost, X., Fei, S.-M.: Identification of three-qubit entanglement. Phys. Rev. A 87, 012316 (2013)

    Article  ADS  Google Scholar 

  45. Breuer, H.P., Petruccione, F.: The Theory of Open Quantum Systems. Oxford University Press, Oxford (2002)

    MATH  Google Scholar 

  46. Sabin, C., Garcia-Alcaine, G.: A classification of entanglement in three-qubit systems. Eur. Phys. J. D 48, 435 (2008)

    Article  MathSciNet  ADS  Google Scholar 

  47. Barreiro, J.T., Muller, M., Schindler, P., Nigg, D., Monz, T., Chwalla, M., Hennrich, M., Roos, C.F., Zoller, P., Blatt, R.: An open-system quantum simulator with trapped ions. Nature (London) 470, 486 (2011)

    Google Scholar 

  48. Brakhane, S., Alt, W., Kampschulte, T., Martinez-Dorantes, M., Reimann, R., Yoon, S., Widera, A., Meschede, D.: Bayesian feedback control of a two-atom spin-state in an atom-cavity system. Phys. Rev. Lett. 109, 173601 (2012)

    Article  ADS  Google Scholar 

Download references

Acknowledgments

This work was supported by the National Natural Science Foundation of China under Grant Nos. 11105001, 11004001, 10975125, the Key Project of Chinese Ministry of Education (Grant No. 212076), and by Anhui Provincial Natural Science Foundation under Grant No. 1408085QA22.

Author information

Authors and Affiliations

  1. School of Electric Engineering and Information, Anhui University of Technology, Ma’anshan, 243002, People’s Republic of China

    Xiao San Ma, Ying Qiao, Mu Tian Cheng & Xiao Dong Liu

Authors
  1. Xiao San Ma
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Ying Qiao
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Mu Tian Cheng
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Xiao Dong Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Xiao San Ma.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Ma, X.S., Qiao, Y., Cheng, M.T. et al. Three-qubit entanglement generation of quantum states dissipating into a common environment. Quantum Inf Process 13, 1879–1891 (2014). https://doi.org/10.1007/s11128-014-0781-3

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11128-014-0781-3

Keywords

Search

Navigation