arXivDaily arXiv每日学术速递 周一至周五更新
arXiv quant-ph/0506107quant-ph
收藏

私有量子信道的极限与约束

Limits and restrictions of private quantum channel

Jan Bouda, Mario Ziman

备注：
23 pages, submitted to QI&C
阅读 PDF
arXiv 页面 ↗HTML 原文 ↗

摘要：

我们研究了单个量子比特上的私有量子信道，它加密给定的明文状态集$P$。具体地，我们确定所有可实现的状态$ρ^{(0)}$（加密的平均输出），并且对于每个特定的集合$P$，我们确定加密该集合所必需且足够的密钥的熵。事实证明，当集合$P$是二维的时，密钥的单个比特是足够的。然而，在三维$P$的情况下，密钥的必要和足够的熵根据状态$ρ^{(0)}$在1和2比特之间连续变化。最后，我们推导出私人量子信道达到这些界限。我们证明了量子比特上的泛非运算的不可能性可以从一个比特的密钥不足以加密量子比特的事实推导出来。

英文摘要：

We study private quantum channels on a single qubit, which encrypt given set of plaintext states $P$. Specifically, we determine all achievable states $ρ^{(0)}$ (average output of encryption) and for each particular set $P$ we determine the entropy of the key necessary and sufficient to encrypt this set. It turns out that single bit of key is sufficient when the set $P$ is two dimensional. However, the necessary and sufficient entropy of the key in case of three dimensional $P$ varies continuously between 1 and 2 bits depending on the state $ρ^{(0)}$. Finally, we derive private quantum channels achieving these bounds. We show that the impossibility of universal NOT operation on qubit can be derived from the fact that one bit of key is not sufficient to encrypt qubit.

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。

↑