量子密钥分发理论的不完备性与极限
Incompleteness and Limit of Quantum Key Distribution Theory
摘要：
在量子密钥分发（QKD）中，许多文献都提出了迹距（$d$）的概念来保证量子密钥分发的通用组合安全性。在这篇导论文章中，首先明确地解释了QKD理论无条件安全性主张中的主要误解。一般来说，造成对担保债权误解的原因是Renner论文中的引理。提出了完美随机密钥的生成由概率$ (1-d)$保证，其失败概率为$d$。因此，当协议成功时，生成的密钥提供了完美的随机密钥序列。因此，QKD为一次性密码本提供了完美的保密性。这就是成分声称的原因。然而，迹距离（或变分距离）的量不是这样的事件的概率。如果$d $不够小，则生成的密钥序列总是不均匀的。如果要使用迹距离，首先需要重新构造迹距离的计算方法，回到基于计算复杂度的不可约性理论，并阐明变分距离的值的意义。此外，对信息论的情况也进行了同样的分析。阮慧萍最近发表的系列论文，已经对这些问题作出了回答。本文对Yuen的理论作了更简洁的描述，并阐明了Tomamichel等人和Hayashi等人最近提出的迹距离上界理论是基于Renner的推理而建立的，不适合作为信息论安全的分析.最后，我们介绍了一种不同原理的宏观量子通信来代替Q比特量子密钥分配。
英文摘要：
It is claimed in the many papers that a trace distance ($d$) guarantees the universal composition security in quantum key distribution (QKD). In this introduction paper, at first, it is explicitly explained what is the main misconception in the claim of the unconditional security for QKD theory. In general terms, the cause of the misunderstanding on the security claim is the Lemma in the paper of Renner. It suggests that the generation of the perfect random key is assured by the probability $ (1-d)$, and its failure probability is $d$. Thus, it concludes that the generated key provides the perfect random key sequence when the protocol suceeds. So the QKD provides perfect secrecy to the one time pad. This is the reason for the composition claim. However, the quantity of the trace distance (or variational distance) is not the probability for such an event. If $d $ is not small enough, always the generated key sequence is not uniform. Now one needs the reconstruction of the evaluation of the trace distance if one wants to use it. One should first go back to the indistinguishability theory in the computational complexity based, and to clarify the meaning of the value of the variational distance. In addition, the same analysis for the information theoretic case is necessary. The recent serial papers by H.P.Yuen have given the answer on such questions. In this paper, we show more concise description of Yuen's theory, and clarify that the recent upper bound theories for the trace distance by Tomamichel et al and Hayashi et al are constructed based on the reasoning of Renner and it is unsuitable as the analysis for information theoretic security. Finally, we introduce a macroscopic quantum communication with different principle to replace Q-bit QKD.
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