发表机构
School of Mathematics, Institute for Research in Fundamental Sciences (IPM); Centre for Quantum Technologies, National University of Singapore; Department of Electrical and Computer Engineering, National University of Singapore（基础科学研究所数学学院; 新加坡国立大学量子技术中心; 新加坡国立大学电气与计算机工程系）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文通过全量子放大引理和低次多项式近似，证明了任意有限维无记忆信道在速率超过量子容量时纠缠传输保真度指数衰减的强逆界。
AI 中文摘要
我们证明了对于每一个有限维无记忆信道，量子通信存在指数级强逆界：在任意固定速率高于量子容量时，每个码的纠缠传输保真度随信道使用次数指数衰减。证明包含两个主要部分。首先，一个全量子放大引理将低保真度码转换为高保真度码，其传输量子比特数的损失由信道斯廷斯普龙膨胀在接收者-环境二分上的正交投影的射影张量范数控制。其次，一个低次多项式构造以指数精度逼近该投影子的张量幂，同时控制其射影范数，为放大论证提供所需的近似。
英文摘要
A quantum channel can transmit quantum states, classical messages, or classical messages that remain secret from its environment. We prove exponential strong converses for all three tasks over arbitrary finite-dimensional memoryless quantum channels, at their respective regularized capacities and allowing arbitrary entangled inputs across channel uses and joint decoding. Above quantum or classical capacity, entanglement fidelity or decoding success probability, respectively, decays exponentially with the number of channel uses. Above private capacity, fidelity to an ideal shared secret key decays exponentially; in particular, vanishing secrecy error forces decoding success to vanish. The proofs combine one-shot quantum blowing-up lemmas, which convert codes with low success into reliable codes with a controlled loss in code size, with a low-degree polynomial approximation of the channel's Stinespring image projector. The loss is governed by the projective tensor norm of the approximation across the receiver--environment bipartition. For memoryless channels, the polynomial construction gives exponential accuracy while keeping the rate loss arbitrarily small, turning the corresponding weak converses into strong converses.
