Springer Nature is making SARS-CoV-2 and COVID-19 research free. View research | View latest news | Sign up for updates

Two-qubit mixed states and teleportation fidelity: purity, concurrence, and beyond

Abstract

To explore the properties of a two-qubit mixed state, we consider quantum teleportation. The fidelity of a teleported state depends on the resource state purity and entanglement, as characterized by concurrence. Concurrence and purity are functions of state parameters. However, it turns out that a state with larger purity and concurrence, may have comparatively smaller fidelity. By computing teleportation fidelity, concurrence and purity for two-qubit X-states, we show it explicitly. We further show that fidelity changes monotonically with respect to functions of parameters – other than concurrence and purity. A state with smaller concurrence and purity, but larger value of one of these functions has larger fidelity. These functions, thus characterize nonlocal classical and/or quantum properties of the state that are not captured by purity and concurrence alone. In particular, concurrence is not enough to characterize the entanglement properties of a two-qubit mixed state.

Graphical abstract

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

References

  1. 1.

    C.H. Bennett, G. Brassard, C. Crépeau, R. Jozsa, A. Peres, W.K. Wootters, Phys. Rev. Lett. 70, 1895 (1993)

  2. 2.

    A.K. Ekert, Phys. Rev. Lett. 67, 661 (1991)

  3. 3.

    M. Hillery, V. Buzek, A. Berthiaume, Phys. Rev. A 59, 1829 (1999)

  4. 4.

    S. Popescu, Phys. Rev. Lett. 72, 797 (1994)

  5. 5.

    K. Życzkowski, P. Horodecki, A. Sanpera, M. Lewenstein, Phys. Rev. A 58, 883 (1988)

  6. 6.

    S. Bose, V. Vedral, Phys. Rev. A 61, 040101(R) (2000)

  7. 7.

    K.G. Paulson, S.V.M Satyanarayana, Phys. Lett. A 381, 1134 (2017)

  8. 8.

    F. Verstraete, H. Verschelde, Phys. Rev. A 66, 022307 (2002)

  9. 9.

    W. Wootters, Phys. Rev. Lett. 80, 2245 (1998)

  10. 10.

    G. Vidal, R.F. Werner, Phys. Rev. A 65, 032314 (2002)

  11. 11.

    C. Datta, A. Das, S. Nandi, P. Agrawal, in preparation

  12. 12.

    J.M. Torres, J.Z. Bernád, Phys. Rev. A 94, 052329 (2016)

  13. 13.

    P.E.M.F. Mendonça, M.A. Marchiolli, D. Galetti, Ann. Phys. 351, 79 (2014)

  14. 14.

    S. Ishizaka, T. Hiroshima, Phys. Rev. A 62, 022310 (2000)

  15. 15.

    T. Yu, J.H. Eberly, Quant. Inf. Comput. 7, 459 (2007)

  16. 16.

    A.R.P. Rau, J. Phys. A Math. Gen.42, 412002 (2009)

Download references

Author information

Correspondence to Sumit Nandi.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Nandi, S., Datta, C., Das, A. et al. Two-qubit mixed states and teleportation fidelity: purity, concurrence, and beyond. Eur. Phys. J. D 72, 182 (2018). https://doi.org/10.1140/epjd/e2018-90252-2

Download citation

Keywords

  • Quantum Information