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arXiv 1102.1678quant-ph
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量子比特承诺的最优界

Optimal bounds for quantum bit commitment

André Chailloux, Iordanis Kerenidis

摘要:

比特承诺是一种基本的密码原语,有着广泛的应用。量子信息允许比特承诺方案在信息理论的设置,其中没有不诚实的一方可以完全欺骗。Ambainis以前最著名的量子协议达到了最多3/4的欺骗概率[Amb 01]。另一方面,Kitaev证明了没有量子协议的欺骗概率可以小于1/sqrt{2} [Kit 03](他对抛硬币的下限可以很容易地扩展到比特承诺)。缩小这一差距一直是一个重要而开放的问题。在本文中,我们提供了量子比特承诺的最佳界。我们首先展示了一个约为0.739的下界,改进了Kitaev的下界。然后,我们提出了一个最佳的量子比特承诺协议,它具有欺骗概率任意接近0.739。更准确地说,我们展示了如何使用任何具有欺骗概率1/2 + eps的弱抛硬币协议,以实现具有欺骗概率0.739 + O(eps)的量子比特承诺协议。然后,我们使用Mochon[Moc 07]描述的最优量子弱硬币翻转协议。为了强调我们的协议使用了弱抛硬币之外的量子效应,我们证明了任何经典的位承诺协议,具有完美的弱(或强)抛硬币的欺骗概率至少为3/4。

英文摘要:

Bit commitment is a fundamental cryptographic primitive with numerous applications. Quantum information allows for bit commitment schemes in the information theoretic setting where no dishonest party can perfectly cheat. The previously best-known quantum protocol by Ambainis achieved a cheating probability of at most 3/4[Amb01]. On the other hand, Kitaev showed that no quantum protocol can have cheating probability less than 1/sqrt{2} [Kit03] (his lower bound on coin flipping can be easily extended to bit commitment). Closing this gap has since been an important and open question. In this paper, we provide the optimal bound for quantum bit commitment. We first show a lower bound of approximately 0.739, improving Kitaev's lower bound. We then present an optimal quantum bit commitment protocol which has cheating probability arbitrarily close to 0.739. More precisely, we show how to use any weak coin flipping protocol with cheating probability 1/2 + eps in order to achieve a quantum bit commitment protocol with cheating probability 0.739 + O(eps). We then use the optimal quantum weak coin flipping protocol described by Mochon[Moc07]. To stress the fact that our protocol uses quantum effects beyond the weak coin flip, we show that any classical bit commitment protocol with access to perfect weak (or strong) coin flipping has cheating probability at least 3/4.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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