We propose a new proof method for direct coding theorems for wiretap channels where the eavesdropper has access to a quantum version of the transmitted signal on an infinite-dimensional Hilbert space and the legitimate parties communicate through a classical channel or a classical input, quantum output (cq) channel. The transmitter input can be subject to an additive cost constraint, which specializes to the case of an average energy constraint. This method yields errors that decay exponentially with increasing block lengths. Moreover, it provides a guarantee of a quantum version of semantic security, which is an established concept in classical cryptography and physical layer security. Therefore, it complements existing works which either do not prove the exponential error decay or use weaker notions of security. The main part of this proof method is a direct coding result on channel resolvability which states that there is only a doubly exponentially small probability that a standard random codebook does not solve the channel resolvability problem for the cq channel. Semantic security has strong operational implications meaning essentially that the eavesdropper cannot use its quantum observation to gather any meaningful information about the transmitted signal. We also discuss the connections between semantic security and various other established notions of secrecy.

翻译：我们提出了一种新的证明方法，用于窃听信道的直接编码定理，其中窃听者能够访问无限维希尔伯特空间上传输信号的量子版本，而合法方则通过经典信道或经典输入、量子输出（cq）信道进行通信。发射输入可以受到加性成本约束，该约束可特指平均能量约束。该方法产生的错误概率随块长度的增加呈指数级衰减。此外，它提供了量子版本语义安全性的保证，这一概念在经典密码学和物理层安全中已是成熟理论。因此，该方法补充了现有工作的不足——这些工作要么未证明指数级误差衰减，要么使用了较弱的安全概念。该证明方法的主要部分是基于信道可分辨性的直接编码结果，该结果表明：对于cq信道，标准随机码本无法解决信道可分辨性问题的概率仅为双重指数级小。语义安全性具有强操作含义，本质上意味着窃听者无法利用其量子观测获取任何关于传输信号的有意义信息。我们还讨论了语义安全性与各种其他现有保密概念之间的联系。