CN 2016: Computer Networks pp 237-246 | Cite as

Quantum Network Protocol for Qudits with Use of Quantum Repeaters and Pauli Z-Type Operational Errors

Conference paper
Part of the Communications in Computer and Information Science book series (CCIS, volume 608)

Abstract

In this paper a quantum communication protocol with use of repeaters is presented. The protocol is constructed for qudits i.e. the generalized quantum information units. One-dit teleportation is based on the generalized Pauli-Z (phase-flip) gate’s correction. This approach avoids using Pauli-X and Hadamard gates unlike in other known protocols based on quantum repeaters which were constructed for qubits and qudits. It is also important to mention that the repeaters based on teleportation protocol, described in this paper, allow a measurement in the standard base (what simplifies the measurement process) and the use of teleportation causes only Pauli-Z operational errors.

Keywords

Quantum information transfer Quantum repreater Qudit teleportation protocol 

Notes

Acknowledgments

We would like to thank for useful discussions with the Q-INFO group at the Institute of Control and Computation Engineering (ISSI) of the University of Zielona Góra, Poland. We would like also to thank to anonymous referees for useful comments on the preliminary version of this paper. The numerical results were done using the hardware and software available at the “GPU \(\mu \)-Lab” located at the Institute of Control and Computation Engineering of the University of Zielona Góra, Poland.

References

  1. 1.
    Stucki, D., Legr, M., Buntschu, F., Clausen, B., Felber, N., Gisin, N., Henzen, L., Junod, P., Litzistorf, G., Monbaron, P., Monat, L., Page, J.-B., Perroud, D., Ribordy, G., Rochas, A., Robyr, S., Tavares, J., Thew, R., Trinkler, P., Ventura, S., Voirol, R., Walenta, N., Zbinden, H.: Long-term performance of the SwissQuantum quantum key distribution network in a field environment. New J. Phys. 13(12), 123001 (2011)CrossRefGoogle Scholar
  2. 2.
    Ritter, S., Nolleke, C., Hahn, C., Reiserer, A., Neuzner, A., Uphoff, M., Mucke, M., Figueroa, E., Bochmann, J., Rempe, G.: An elementary quantum network of single atoms in optical cavities. Nature 484, 195–200 (2012)CrossRefGoogle Scholar
  3. 3.
    Nikolopoulos, G.M., Jex, I.: Quantum State Transfer and Network Engineering. Springer, Heidelberg (2014)CrossRefMATHGoogle Scholar
  4. 4.
    Briegel, H.J., Dür, W., Cirac, J.I., Zoller, P.: Quantum repeaters: the role of imperfect local operations in quantum communication. Phys. Rev. Lett. 81(26), 5932 (1998)CrossRefGoogle Scholar
  5. 5.
    van Meter, R., Touch, J., Horsman, C.: Recursive quantum repeater networks. Prog. Inform. 8, 65–79 (2011)CrossRefGoogle Scholar
  6. 6.
    van Meter, R.: Quantum Networking. Wiley, Hoboken (2014)CrossRefMATHGoogle Scholar
  7. 7.
    Sangouard, N., Simon, C., de Riedmatten, H., Gisin, N.: Quantum repeaters based on atomic ensembles and linear optics. Rev. Mod. Phys. 83, 33–80 (2011)CrossRefGoogle Scholar
  8. 8.
    Ursin, R., Tiefenbacher, F., Schmitt-Manderbach, T., Weier, H., Scheidl, T., Lindenthal, M., Blauensteiner, B., Jennewein, T., Perdigues, J., Trojek, P., Ömer, B., Fürst, M., Meyenburg, M., Rarity, J., Sodnik, Z., Barbieri, C., Weinfurter, H., Zeilinger, A.: Entanglement-based quantum communication over 144 km. Nat. Phys. 3, 481–486 (2007)CrossRefGoogle Scholar
  9. 9.
    Hirvensalo, M.: Quantum Computing. Springer, Heidelberg (2001)CrossRefMATHGoogle Scholar
  10. 10.
    Klamka, J., Węgrzyn, S., Znamirowski, L., Winiarczyk, R., Nowak, S.: Nano and quantum systems of informatics. Bull. Pol. Acad. Sci. Tech. Sci. 52(1), 1–10 (2004)MATHGoogle Scholar
  11. 11.
    Klamka, J., Węgrzyn, S., Bugajski, S.: Foundation of quantum computing. Archiwum Informatyki Teoretycznej i Stosowanej 1(2), 97–142 (2001)Google Scholar
  12. 12.
    Klamka, J., Węgrzyn, S., Bugajski, S.: Foundation of quantum computing. Archiwum Informatyki Teoretycznej i Stosowanej. Part 2 14(2), 93–106 (2002)Google Scholar
  13. 13.
    Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information. Cambridge University Press, New York (2000)MATHGoogle Scholar
  14. 14.
    Duan, L.M., Lukin, M.D., Cirac, J.I., Zoller, P.: Long-distance quantum communication with atomic ensembles and linear optics. Nature 414, 413–418 (2011)CrossRefGoogle Scholar
  15. 15.
    Jiang, L., Taylor, J.M., Nemoto, K., Munro, W.J., van Meter, R., Lukin, M.D.: Quantum repeater with encoding. Phys. Rev. A 79, 032325 (2009)CrossRefGoogle Scholar
  16. 16.
    Munro, W.J., Stephens, A.M., Devitt, S.J., Harrison, K.A., Nemoto, K.: Quantum communication without the necessity of quantum memories. Nat. Photonics 6, 777–781 (2012)CrossRefGoogle Scholar
  17. 17.
    Muralidharan, S., Kim, J., Lütkenhaus, N., Lukin, M.D., Jiang, L.: Ultrafast and fault-tolerant quantum communication across long distances. Phys. Rev. Lett. 112, 250501 (2014)CrossRefGoogle Scholar
  18. 18.
    Aliferis, P., Leung, D.W.: Computation by measurements: A unifying picture. Phys. Rev. A 70(6), 062314 (2004)CrossRefGoogle Scholar
  19. 19.
    Knill, E.: Quantum computing with realistically noisy devices. Nature 434, 39–44 (2005)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.Institute of Control and Computation EngineeringUniversity of Zielona GóraZielona GóraPoland
  2. 2.Institute of Information Systems, Faculty of CyberneticsMilitary University of TechnologyWarsawPoland

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