量子安全直接通信直接利用量子态和量子信道等量子资源实现保密通信。 其基于量子态不可克隆原理，可对未知信道进行感知，利用合法接收方与非法接收方之间的信道差异，实现经典消息的保密传输。 近年来量子安全直接通信在实用化上取得了长足的进步，但在有限码长条件下的安全性一直未能得到完全的解决。 本论文研究了量子安全直接通信的有限长理论，并对其安全性进行分析。 首先，本文研究了有限长量子搭线信道理论，该理论是分析量子安全直接通信和量子密钥分发的基础理论工具。 本论文通过将逆哈希与任意纠错码级联构造出了模块化搭线信道码，分析了固定码率下错误概率和信息泄露量随码长增加的指数收敛速度，其中得到的收敛速度比Hayashi2015年得到的结果更快。 相比于Hayashi的搭线信道码，该模块化搭线信道码不依赖于纠错码的具体结构，具有高度的灵活性，且在实际应用中更加方便。 其次，为了从更加一般的角度研究量子安全直接通信，本文发展了安全密集编码模型。 从一个Alice，Bob，Eve共享的任意态开始，Alice可从一个群中选择幺正操作将经典消息编码在该共享态上并发送给Bob，Bob随后进行测量读出经典消息。 该模型考虑了Eve截获Alice发出的全部量子态这一最坏情况下的安全性。 本文定义了完备性，可靠性和安全性作为该模型的性能指标，并在有限长条件下推导出了这些指标与量子搭线信道理论的相应指标之间的转化关系，该转化关系进一步揭示了安全密集编码模型与量子搭线信道两者容量的等价性。 最后，本文将安全密集编码模型用于量子安全直接通信的性能分析。安全密集编码模型未能描述共享态的产生方式，而量子安全直接通信则对态的分发与验证进行了刻画。利用此特性，本文详细分析了在高维两步协议中如何对一般的共享态做参数估计。结合参数估计的结果与安全密集编码的分析可以给出高维两步协议在有限长条件下的安全性。该分析模式可从高维两步协议自然地退化到更加特殊的两步协议和DL04协议，具有较高的普适性。特别地，在DL04协议上得到的结果可以指导大量实际通信系统中的有限长安全性评估，该方法对其他类似的协议也有较高的参考价值。
Quantum secure direct communication (QSDC) is aimed to implement secure transmission of classical messages by exploiting quantum resources. The no-cloning theorem makes it possible to probe an unknown quantum channel. The difference between the legitimate channel and the illegitimate channel enables us to transmit secret messages. Although QSDC has achieved great progress in terms of experiments and practical application in recent years, the security analysis in practical situations is not completely resolved yet. This thesis studies finite-blocklength theory of QSDC to analyze the security under finite-length coding.At first, nonasymptotic quantum wiretap channel theory is investigated, which acts as a fundamental tool of QSDC. We construct a modular wiretap code by concatenating inverse universal hash function and any error correction code and, under a fixed sacrificed rate, obtain the exponential decreasing rate of information leakage, which is better than existing results. In contrast to non-modular wiretap code, the modular code is more flexible and convenient for application thanks to the independence of the special structure of error correction code.Then, to explore QSDC from a more general viewpoint, a private dense coding model is proposed. The model starts from a general quantum state shared by Alice, Bob, and Eve. Alice is allowed to encode classical information on the state by applying an operation chosen from a given group and send her parts to Bob. After receiving, Bob can measure the joint state to read out the information. The model considers the security in the worst case that Eve intercepts all states sent by Alice. To evaluate the model, we define completeness, security, and reliability as the performance indicators and derived their correlation with quantum wiretap channels, which further implies the equivalence of their respective capacities. Finally, the private dense coding model is applied to obtain the performance of QSDC. While private dense coding model does not characterize the generation of preshared states, QSDC provides additional state distribution and verification processes. By exploiting these processes, the parameter estimation for general states in high-dimensional two-step protocol is analyzed, which leads to the security in finite-length regime after combined with the results in private dense coding. The analysis is then reduced to two-step protocol and DL04 protocol. Specifically, the result of DL04 protocol should be useful for the finite-length evaluation of most of the practical QSDC systems and can be a good reference for other related protocols.
