Skip to main content

Evaluation of the performance of two state-transfer Hamiltonians in the presence of static disorder

Quantum Information Processing volume 15, pages 2553–2568 (2016)Cite this article

Abstract

We analyze the performance of two quantum-state-transfer Hamiltonians in the presence of diagonal and off-diagonal disorders, and in terms of different measures. The first Hamiltonian pertains to a fully engineered chain, and the second to a chain with modified boundary couplings. The task is to find which Hamiltonian is the most robust to given levels of disorder and irrespective of the input state. In this respect, it is shown that the performances of the two protocols are approximately equivalent.

This is a preview of subscription content, access via your institution.

Access options

Buy single article

Instant access to the full article PDF.

USD 39.95

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7

Notes

  1. Strictly speaking, for the spin-analogue Hamiltonian one does not need the assumption for the chain to be initially prepared in the ground (vacuum) state. State transfer is expected to take place irrespective of the initial state of the chain, provided that the input spin (site) is initially decorrelated from the rest of the chain (e.g., see chapter 2 in [1]). The main reason is that the evolution operator at the transfer time reduces to a permutation (up perhaps to an unimportant global phase).

References

  1. Nikolopoulos, G.M., Jex, I. (eds.): Quantum State Transfer and Network Engineering. Quantum Science and Technology, Springer, Heidelberg (2014)

  2. Nikolopoulos, G.M., Petrosyan, D., Lambropoulos, P.: Electron wavepacket propagation in a chain of coupled quantum dots. J. Phys. Condens. Matter 16, 4991–5002 (2004)

    Article  ADS  Google Scholar 

  3. Nikolopoulos, G.M., Petrosyan, D., Lambropoulos, P.: Coherent electron wavepacket propagation and entanglement in array of coupled quantum dots. Europhys. Lett. 65, 297–303 (2004)

    Article  ADS  Google Scholar 

  4. Christandl, M., Datta, N., Ekert, A., Landahl, A.J.: Perfect state transfer in quantum spin networks. Phys. Rev. Lett. 92, 187902 (2004)

    Article  ADS  Google Scholar 

  5. Banchi, L., Apollaro, T.J.G., Cuccoli, A., Vaia, R., Verrucchi, P.: Optimal dynamics for quantum-state and entanglement transfer through homogeneous quantum systems. Phys. Rev. A 82, 052321 (2010)

    Article  ADS  Google Scholar 

  6. Banchi, L., Apollaro, T.J.G., Cuccoli, A., Vaia, R., Verrucchi, P.: Long quantum channels for high-quality entanglement transfer. New J. Phys. 13, 123006 (2011)

    Article  ADS  Google Scholar 

  7. Banchi, L., Bayat, A., Verrucchi, P., Bose, S.: Nonperturbative entangling gates between distant qubits using uniform cold atom chains. Phys. Rev. Lett. 106, 140501 (2011)

    Article  ADS  Google Scholar 

  8. Zwick, A., Álvarez, G.A., Stolze, J., Osenda, O.: Spin chains for robust state transfer: modified boundary couplings versus completely engineered chains. Phys. Rev. 85, 012318 (2012)

    Article  ADS  Google Scholar 

  9. Stolze, J., Álvarez, G.A., Osenda, O., Zwick, A.: Robustness of spin-chain state-transfer schemes. In: Nikolopopulos, G.M., Jex, I. (eds.) Quantum State Transfer and Quantum Network Engineering, pp. 149–182. Quantum Science and Technology, Springer, Heidelberg (2014)

    Chapter  Google Scholar 

  10. Nikolopoulos, G.M.: Statistics of a quantum-state-transfer Hamiltonian in the presence of disorder. Phys. Rev. A 87, 042311 (2013)

    Article  ADS  Google Scholar 

  11. Jordan, P., Wigner, E.: Über das Paulische Äquivalenzverbot. Z. Phys. 47, 631–651 (1928)

    Article  ADS  MATH  Google Scholar 

  12. Sachdev, S.: Quantum Phase Transitions. Cambridge University Press, Cambridge (1999)

    MATH  Google Scholar 

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

    MATH  Google Scholar 

  14. Petrosyan, D., Nikolopoulos, G.M., Lambropoulos, P.: State transfer in static and dynamic spin chains with disorder. Phys. Rev. A 81, 042307 (2010)

    Article  ADS  Google Scholar 

  15. Bose, S.: Quantum communication through an unmodulated spin chain. Phys. Rev. Lett. 91, 207901 (2003)

    Article  ADS  Google Scholar 

  16. Bose, S.: Quantum communication through spin chain dynamics: an introductory overview. Contemp. Phys. 48, 13–30 (2007)

    Article  ADS  Google Scholar 

  17. Romito, A., Fazio, R., Bruder, C.: Solid-state quantum communication with Josephson arrays. Phys. Rev. B 71, 100501(R) (2005)

    Article  ADS  Google Scholar 

  18. Yang, S., Bayat, A., Bose, S.: Spin-state transfer in laterally coupled quantum-dot chains with disorders. Phys. Rev. A 82, 022336 (2010)

    Article  ADS  Google Scholar 

  19. Wootters, W.K.: Entanglement of formation of an arbitrary state of two qubits. Phys. Rev. Lett. 80, 2245–2248 (1998)

    Article  ADS  Google Scholar 

  20. Bayat, A., Bose, S.: Information-transferring ability of the different phases of a finite XXZ spin chain. Phys. Rev. A 81, 012304 (2010)

    Article  ADS  Google Scholar 

  21. Horodecki, M., Horodecki, P., Horodecki, R.: General teleportation channel, singlet fraction, and quasidistillation. Phys. Rev. A 60, 1888–1898 (1999)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  22. Massar, S., Popescu, S.: Optimal extraction of information from finite quantum ensembles. Phys. Rev. Lett. 74, 1259–1263 (1995)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  23. De Chiara, G., Rossini, D., Montangero, S., Fazio, R.: From perfect to fractal transmission in spin chains. Phys. Rev A 72, 012323 (2005)

    Article  ADS  Google Scholar 

  24. Cappellaro, P.: Implementation of state transfer Hamiltonians in spin chains with magnetic resonance techniques. In: Nikolopopulos, G.M., Jex, I. (eds.) Quantum State Transfer and Quantum Network Engineering, pp. 183–222. Quantum Science and Technology, Springer, Heidelberg (2014)

    Chapter  Google Scholar 

  25. Bellec, M., Nikolopoulos, G.M., Tzortzakis, S.: State transfer hamiltonians in photonic lattices. In: Nikolopopulos, G.M., Jex, I. (eds.) Quantum State Transfer and Quantum Network Engineering, pp. 223–245. Quantum Science and Technology, Springer, Heidelberg (2014)

    Chapter  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Electronic Structure & Laser, FORTH, P.O. Box 1385, 70013, Heraklion, Greece

    A. K. Pavlis, G. M. Nikolopoulos & P. Lambropoulos

  2. Department of Physics, University of Crete, P.O. Box 2208, 71003, Heraklion, Crete, Greece

    A. K. Pavlis & P. Lambropoulos

Authors
  1. A. K. Pavlis
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. G. M. Nikolopoulos
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. P. Lambropoulos
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to G. M. Nikolopoulos.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Pavlis, A.K., Nikolopoulos, G.M. & Lambropoulos, P. Evaluation of the performance of two state-transfer Hamiltonians in the presence of static disorder. Quantum Inf Process 15, 2553–2568 (2016). https://doi.org/10.1007/s11128-016-1287-y

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11128-016-1287-y

Keywords

  • State transfer
  • Quantum communication
  • Spin chains