Pseudorandom Quantum States
Pseudorandom Quantum States
复制标题
伪随机量子态
DOI：
10.1007/978-3-319-96878-0_5
复制
发表时间：
2018
期刊：
影响因子：
--
通讯作者：
Song, Fang
中科院分区：
文献类型：
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作者：
Ji, Zhengfeng;Liu, Yi-Kai;Song, Fang
我们提出了伪随机量子态的概念，它对任何量子多项式时间对手都是随机的。它提供了计算近似的完全随机量子态类似的精神上的密码伪随机发生器，而不是以前已经研究过的量子伪随机性的概念，如量子设计类似于明智的独立distributions.Under量子安全的单向函数存在的假设下，我们提出了有效的伪随机态的结构，表明我们的定义是可实现的。然后，我们证明了伪随机状态的几个基本性质，这表明我们的定义的效用。首先，我们证明了一个密码学不可克隆定理：当给定多项式多个副本作为输入时，没有有效的量子算法可以创建伪随机状态的额外副本。其次，正如对随机量子态所预期的那样，我们证明了伪随机量子态平均是高度纠缠的。最后，作为一个主要的应用，我们证明了任何一族的伪随机态都能自然地产生一个私钥量子货币方案。
We propose the concept of pseudorandom quantum states, which appear random to any quantum polynomial-time adversary. It offers acomputationalapproximation to perfectly random quantum states analogous in spirit to cryptographic pseudorandom generators, as opposed tostatisticalnotions of quantum pseudorandomness that have been studied previously, such as quantumt-designs analogous tot-wise independent distributions.Under the assumption that quantum-secure one-way functions exist, we present efficient constructions of pseudorandom states, showing that our definition is achievable. We then prove several basic properties of pseudorandom states, which show the utility of our definition. First, we show a cryptographic no-cloning theorem: no efficient quantum algorithm can create additional copies of a pseudorandom state, when given polynomially-many copies as input. Second, as expected for random quantum states, we show that pseudorandom quantum states are highly entangled on average. Finally, as a main application, we prove that any family of pseudorandom states naturally gives rise to a private-key quantum money scheme.