arXiv quant-ph/03051542003-05quant-ph

量子记忆的力量

On the Power of Quantum Memory

Robert Koenig, Ueli Maurer, Renato Renner

备注：: 11 pages; references added and notation simplified; to appear in the July 2005 issue of IEEE Transactions on Information Theory
发表信息：: IEEE Trans. Inf. Th., vol. 51, no. 7 (2005)
DOI：: 10.1109/TIT.2005.850087

摘要：

我们解决的问题是量子存储器是否比经典存储器更强大。特别地，我们考虑一种设置，其中关于随机n比特串X的信息存储在r个经典或量子比特中，其中r<n，即，所存储的信息必然只是部分的。稍后，询问关于X的随机选择的二进制问题F，其必须仅使用存储的信息来回答。然后，分别针对存储设备是经典的或量子力学的情况，比较正确猜测答案F（X）的最大概率。我们表明，尽管量子比特的测量可以任意依赖于要回答的问题F，但对于小的差值n-r，量子优势已经可以忽略不计。密码学的一个含义是，当对手的记忆被允许是r个量子比特而不仅仅是r个经典比特时，通过应用从两个通用类的哈希函数中公开选择的将n比特字符串映射到s比特字符串（对于某些s<n-r）的压缩函数来放大隐私，基本上保持同样的安全性。

英文摘要：

We address the question whether quantum memory is more powerful than classical memory. In particular, we consider a setting where information about a random n-bit string X is stored in r classical or quantum bits, for r<n, i.e., the stored information is bound to be only partial. Later, a randomly chosen binary question F about X is asked, which has to be answered using only the stored information. The maximal probability of correctly guessing the answer F(X) is then compared for the cases where the storage device is classical or quantum mechanical, respectively. We show that, despite the fact that the measurement of quantum bits can depend arbitrarily on the question F to be answered, the quantum advantage is negligible already for small values of the difference n-r. An implication for cryptography is that privacy amplification by application of a compression function mapping n-bit strings to s-bit strings (for some s<n-r), chosen publicly from a two-universal class of hash functions, remains essentially equally secure when the adversary's memory is allowed to be r quantum rather than only r classical bits.

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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