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Applied Mechanics and Materials

Loss-and-Noise Tolerant Single-Shot Quantum Coin Flipping

Sheng Bo Huang, Sheng Zhang, Jun Bo Chen, Ding Yi Ji, Jin Liu, Wen Ye

Published Jan 1, 2014• 0 citations
Publisher

Abstract

To make quantum coin flipping protocols more practical, we propose a new method that makes single-shot quantum coin flipping (SS-QCF) protocols tolerant of loss and noise. First, we present a new SS-QCF protocol which is a modification version of the previous one by Berlín et al.[ Phys. Rev. A Vol. 80 (2009), p. 062321]. Next, we prove that our protocol performs well against loss and noise. It shows that the presented protocol is able to be applied in real-world channels.

DOI
10.4028/www.scientific.net/amm.496-500.2332

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To make quantum coin flipping protocols more practical, we propose a new method that makes single-shot quantum coin flipping (SS-QCF) protocols tolerant of loss and noise. First, we present a new SS-QCF protocol which is a modification version of the previous one by Berlín et al.[ Phys. Rev. A Vol. 80 (2009), p. 062321]. Next, we prove that our protocol performs well against loss and noise. It shows that the presented protocol is able to be applied in real-world channels.
So far, most existing single-shot quantum coin flipping (QCF) protocols have failed in a noisy quantum channel. Here, we present a nested-structure framework that makes it possible to achieve partially noise-tolerant QCF, due to a trade-off between the security and the justice correctness. It is showed that noise-tolerant single-shot QCF protocols can be produced by filling the presented framework up with existing or even future protocols. We also proved a lower bound of 0.25, with which a cheating Alice or Bob could bias the outcome.
Coin flipping is a cryptographic primitive in which two distrustful parties wish to generate a random bit to choose between two alternatives. This task is impossible to realize when it relies solely on the asynchronous exchange of classical bits: one dishonest player has complete control over the final outcome. It is only when coin flipping is supplemented with quantum communication that this problem can be alleviated, although partial bias remains. Unfortunately, practical systems are subject to loss of quantum data, which allows a cheater to force a bias that is complete or arbitrarily close to complete in all previous protocols and implementations. Here we report on the first experimental demonstration of a quantum coin-flipping protocol for which loss cannot be exploited to cheat better. By eliminating the problem of loss, which is unavoidable in any realistic setting, quantum coin flipping takes a significant step towards real-world applications of quantum communication. When two spatially separated parties flip a coin, it is impossible to choose between two alternatives in an unbiased manner. This study presents a quantum coin-flipping protocol that overcomes this problem and ensures a dishonest party cannot bias the outcome completely.
Coin flipping is a cryptographic primitive in which two spatially separated players, who in principle do not trust each other, wish to establish a common random bit. If we limit ourselves to classical communication, this task requires either assumptions on the computational power of the participants or it requires them to send messages to each other with sufficient simultaneity to force their complete independence. Without such assumptions, all classical protocols are so that one dishonest player can completely bias the outcome to his choosing. If we allow for quantum communication, on the other hand, protocols have been introduced that limit the maximal bias that dishonest players can produce. However, those protocols would be very difficult to implement in practice because they cannot tolerate realistic losses on the quantum channel between the participants or in their quantum storage and measurement apparatus. In this paper, we introduce a novel quantum protocol and we prove its unconditional security even when such losses are taken into account.
Coin flipping is a cryptographic primitive in which two spatially separated players, who in principle do not trust each other, wish to agree on a random bit. Classical and quantum coin flipping protocols have been studied extensively for more than twenty‐five years. However, until recently, quantum coin flipping protocols were designed without taking into consideration the losses of quantum information that would be unavoidable in any realistic implementation. We introduced in 2008 a novel protocol and proved its security even when losses are taken into account: no cheating player could obtain a desired outcome with a probability greater than (6+2)/8≈93%. Here, we refine our earlier protocol by making it fair in the sense that the optimal cheating strategies allow either player to bias the outcome by the same amount. Specifically, either player can cheat to obtain a desired outcome with probability exactly 90%, but no more. An implementation is underway.
In this paper, we present a loss-tolerant quantum strong coin flipping protocol with bias 0.359. This is an improvement over Berlin etal's protocol [BBBG08] which achieves a bias of 0.4. To achieve this, we extend Berlin et al.'s protocol by adding an encryption step that hides some information to Bob until he confirms that he successfully measured. We also show using numerical analysis that a we cannot improve this bias by considering a k-fold repetition of Berlin etal's protocol for k > 2.