Quantum privacy amplification is a central task in quantum cryptography. Given shared randomness, which is initially correlated with a quantum system held by an eavesdropper, the goal is to extract uniform randomness which is decoupled from the latter. The optimal rate for this task is known to satisfy the strong converse property and we provide a lower bound on the corresponding strong converse exponent. In the strong converse region, the distance of the final state of the protocol from the desired decoupled state converges exponentially fast to its maximal value, in the asymptotic limit. We show that this necessarily leads to totally insecure communication by establishing that the eavesdropper can infer any sent messages with certainty, when given very limited extra information. In fact, we prove that in the strong converse region, the eavesdropper has an exponential advantage in inferring the sent message correctly, compared to the achievability region. Additionally we establish the following technical result, which is central to our proofs, and is of independent interest: the smoothing parameter for the smoothed max-relative entropy satisfies the strong converse property.
翻译:量子私隐放大是量子加密中的一项核心任务。 共享随机性, 最初与窃听器持有的量子系统相关, 目标是提取与后者脱钩的统一随机性。 众所周知, 这项任务的最佳速度是满足强大的反向属性, 我们在相应的强反反向动词上提供了较低的约束。 在强大的反向区域, 协议的最后状态与预期的分解状态之间的距离在无症状限制下, 快速地接近其最大值。 我们证明, 这必然会导致完全不安全的通信, 确定窃听器在得到非常有限的额外信息时, 可以肯定地推断发送的任何信息。 事实上, 我们证明, 在强大的反向区域, 窃听器与可接收性区域相比, 在正确推断发送的信息时具有指数优势。 此外, 我们确定了以下技术结果, 这对于我们的证据至关重要, 并且具有独立的兴趣: 平滑的 最大正弦化的正弦化的正弦化磁质质的参数 。