通过零私有容量量子信道进行私有通信
Private communication via zero-private-capacity quantum channels
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中文总结 AI 辅助
本文通过构造两个零私有容量信道的联合使用实现超激活，证明私有容量不能单独决定信道安全通信价值，并给出超过0.0001903私有比特的编码方案。
中文摘要 AI 辅助
在噪声量子信道上进行私有通信，需要向接收方可靠传输并对环境保密。两个私有容量均为零的信道能否联合实现私有通信，是量子信息论中长期悬而未决的问题。本文通过展示一个四能级信道和一个擦除概率为二分之一的量子比特擦除信道（两者私有容量均为零）解决了该问题，它们的联合使用每次乘积使用可实现超过0.0001903个私有比特。该编码使接收方获得线性信息增益，同时环境泄漏至多为二次，通过固定的联合测量和经典编码实现隐私。这种超激活现象对于独立的经典无记忆窃听信道是不可能的，表明信道的私有容量本身并不能决定其在安全通信中的价值。初始激活示例是通过与大型语言模型的交互发现的，结果已在Lean 4中形式化验证。
英文摘要
Private communication over a noisy quantum channel requires reliable transmission to the receiver and secrecy from the environment. Whether two channels with zero private capacity can jointly enable private communication is a longstanding open problem in quantum information theory. Here we resolve this problem by exhibiting a four-level channel and a qubit erasure channel with half erasure probability, each with zero private capacity, whose joint use achieves more than 0.0001903 private bits per product use. The encoding gives the receiver a linear information gain with at most quadratic environmental leakage, enabling privacy through a fixed joint measurement and classical coding. This superactivation, impossible for independent classical memoryless wiretap channels, shows that a channel's private capacity alone does not determine its value for secure communication. The initial activation example was identified through interactions with large language models, and the result has been formalized in Lean 4.
发表机构
- QudeLeap Research（量子跃迁研究）
- Thrust of Artificial Intelligence, Information Hub,The Hong Kong University of Science and Technology (Guangzhou)（香港科技大学（广州）信息枢纽人工智能组）
机构由 AI 辅助整理，请以论文原文为准。
