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arXiv:quant-ph/0210079 · Physical Review A

Solving the liar detection problem using the four-qubit singlet state

Adán Cabello

Published Jul 7, 2003• 40 citations
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Abstract

A method for solving the Byzantine agreement problem [M. Fitzi, N. Gisin, and U. Maurer, Phys. Rev. Lett. 87, 217901 (2001)] and the liar detection problem [A. Cabello, Phys. Rev. Lett. 89, 100402 (2002)] is introduced. The main advantages of this protocol are that it is simpler and is based on a four-qubit singlet state already prepared in the laboratory.

DOI
10.1103/physreva.68.012304

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A method for solving the Byzantine agreement problem [M. Fitzi, N. Gisin, and U. Maurer, Phys. Rev. Lett. 87, 217901 (2001)] and the liar detection problem [A. Cabello, Phys. Rev. Lett. 89, 100402 (2002)] is introduced. The main advantages of this protocol are that it is simpler and is based on a four-qubit singlet state already prepared in the laboratory.
Quantum mechanics provides several methods to generate and securely distribute private lists of numbers suitably correlated to solve the Three Byzantine Generals Problem. So far, these methods are based on three-qutrit singlet states, four-qubit entangled states, and three or two pairwise quantum key distribution channels. Here we show that the problem can be solved using a single qutrit. This scheme presents some advantages over previous schemes, and emphasizes the specific role of qutrits in basic quantum information processing.
In distributed computing,Byzantine agreement is a practical method to solve its fault-tolerance problem.There is a variation of the Byzantine agreement which is called detectable Byzantine agreement.This kind of protocol is unsolvable by classical means,but can be solved using quantum resources——quantum entangled states.A typical quantum detectable Byzantine agreement is the GBKCW protocol.The part with the generation and distribution of the lists in the GBKCW protocol was dealed with.In order to keep the GBKCW protocol from the intercept-and-resend strategy,the property of the determination of entangled states were employed to test the sharing state between the parties.