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arXiv:quant-ph/0203119 · Physical Review Letters

N -Particle N -Level Singlet States: Some Properties and Applications

Adán Cabello

Published Aug 19, 2002• 119 citations
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Abstract

Three apparently unrelated problems which have no solution using classical tools are described: the "N-strangers," "secret sharing," and "liar detection" problems. A solution for each of them is proposed. Common to all three solutions is the use of quantum states of total spin zero of N spin-(N-1)/2 particles.

DOI
10.1103/physrevlett.89.100402

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Three apparently unrelated problems which have no solution using classical tools are described: the "N-strangers," "secret sharing," and "liar detection" problems. A solution for each of them is proposed. Common to all three solutions is the use of quantum states of total spin zero of N spin-(N-1)/2 particles.
I give a simple argument that demonstrates that the state $\ensuremath{\mid}0⟩\ensuremath{\mid}1⟩+\ensuremath{\mid}1⟩\ensuremath{\mid}0⟩$, with $\ensuremath{\mid}0⟩$ denoting a state with 0 particles (or photons) and $\ensuremath{\mid}1⟩$ a one-particle state, is entangled in spite of recent claims to the contrary. I also discuss viewpoints on the old controversy about whether the above state can be said to display single-particle or single-photon nonlocality.
This paper designs quantum circuit to detect the fault components in the Byzantine generals problem. This circuit is verification circuit that can investigate the equivalence of quantum input particles. In this problem, reach agreement and liar detection are two major issues. In the quantum field, quantum secret sharing can support a special correlation among sharing party. By using this relation, quantum circuit can detect the behavior of the traitor to obtain the consistence of the Byzantine agreement. In regard to the performance, quantum solution can obtain little message exchange and more tolerant faulty components. Furthermore, the proposed circuit is scalable.