Quantum leader election

Article

Abstract

A group of n individuals \(A_{1},\ldots A_{n}\) who do not trust each other and are located far away from each other, want to select a leader. This is the leader election problem, a natural extension of the coin flipping problem to n players. We want a protocol which will guarantee that an honest player will have at least \(\frac{1}{n}-\epsilon \) chance of winning (\(\forall \epsilon >0\)), regardless of what the other players do (whether they are honest, cheating alone or in groups). It is known to be impossible classically. This work gives a simple algorithm that does it, based on the weak coin flipping protocol with arbitrarily small bias derived by Mochon (Quantum weak coin flipping with arbitrarily small bias, arXiv:0711.4114, 2000) in 2007, and recently published and simplified in Aharonov et al. (SIAM J Comput, 2016). A protocol with linear number of coin flipping rounds is quite simple to achieve; we further provide an improvement to logarithmic number of coin flipping rounds. This is a much improved journal version of a preprint posted in 2009; the first protocol with linear number of rounds was achieved independently also by Aharon and Silman (New J Phys 12:033027, 2010) around the same time.

Keywords

Leader election Quantum leader elections Quantum coin flipping 

Notes

Acknowledgements

I would like to thank my adviser Prof. Dorit Aharonov for her support and guidance and for her remarks on this paper (in its many versions) and also thank Prof. Michael Ben–Or for his help.

References

  1. 1.
    Ambainis, A., Buhrman, H., Dodis, Y., Roehrig, H.: Multiparty quantum coin flipping. arXiv:quant-ph/0304112 (2003)
  2. 2.
    Aharon, N., Silman, J.: Quantum dice rolling: a multi-outcome generalization of quantum coin flipping. New J. Phys. 12(3), 033027 (2010)Google Scholar
  3. 3.
    Aharonov, D., Chailloux, A., Ganz, M., Kerenidis, I., Magnin, L.: A simpler proof of existence of quantum weak coin flipping with arbitrarily small bias. SIAM J. Comput. 45(3), 663–679 (2016)MathSciNetCrossRefMATHGoogle Scholar
  4. 4.
    Aharonov, D., Ta-Shma, A., Vazirani, U., Yao, A.: Quantum bit escrow. In: Proceedings of the Thirty-Second Annual ACM Symposium on Theory of Computing, pp. 705–714. ACM (2000)Google Scholar
  5. 5.
    Chailloux, A., Kerenidis, I.: Optimal quantum strong coin flipping. arXiv:0904.1511 (2009)
  6. 6.
    Cleve, R.: Limits on the security of coin flips when half the processors are faulty. In: Proceedings of the 18th Annual ACM Symposium on Theory of Computing, STOC (87), pp. 364–369Google Scholar
  7. 7.
    Feige, U.: Noncryptographic selection protocols. In: 40th Annual Symposium on Foundations of Computer Science, 1999, pp. 142–152. IEEE (1999)Google Scholar
  8. 8.
    Ganz, M., Sattath, O.: Quantum coin hedging (2017, to be published)Google Scholar
  9. 9.
    Mochon, C.: Quantum weak coin flipping with arbitrarily small bias. arXiv:0711.4114 (2000)
  10. 10.
    Mochon, C.: Quantum weak coin-flipping with bias of 0.192. In: Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science, pp. 250–259 (2004)Google Scholar
  11. 11.
    Mayers, D., Salvail, L., Chiba-Kohno, Y.: Unconditionally secure quantum coin tossing. In: Technical Report. arXiv:quant-ph/9904078 (1999)
  12. 12.
    Molina, A., Watrous, J.: Hedging bets with correlated quantum strategies. Proc. R. Soc. A 468(2145), 2614–2629 (2012)ADSMathSciNetCrossRefGoogle Scholar
  13. 13.
    Tani, S., Kobayashi, H., Matsumoto, K.: Exact quantum algorithms for the leader election problem. arXiv.0712.4213 (2007)

Copyright information

© Springer Science+Business Media New York 2017

Authors and Affiliations

  1. 1.The Hebrew UniversityJerusalemIsrael

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