Quantum leader election A group of n individuals $$A_{1},\ldots A_{n}$$ A 1 , … 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 $$\frac{1}{n}-\epsilon$$ 1 n - ϵ chance of winning ( $$\forall \epsilon >0$$ ∀ ϵ > 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Quantum Information Processing Springer Journals

, Volume 16 (3) – Feb 2, 2017
17 pages

Publisher
Springer Journals
Subject
Physics; Quantum Information Technology, Spintronics; Quantum Computing; Data Structures, Cryptology and Information Theory; Quantum Physics; Mathematical Physics
ISSN
1570-0755
eISSN
1573-1332
D.O.I.
10.1007/s11128-017-1528-8
Publisher site
See Article on Publisher Site

Abstract

A group of n individuals $$A_{1},\ldots A_{n}$$ A 1 , … 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 $$\frac{1}{n}-\epsilon$$ 1 n - ϵ chance of winning ( $$\forall \epsilon >0$$ ∀ ϵ > 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.

Journal

Quantum Information ProcessingSpringer Journals

Published: Feb 2, 2017

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