Secret-key distillation from quantum states and channels is a central task of interest in quantum information theory, as it facilitates private communication over a quantum network. Here, we study the task of secret-key distillation from bipartite states and point-to-point quantum channels using local operations and one-way classical communication (one-way LOCC). We employ the resource theory of unextendible entanglement to study the transformation of a bipartite state under one-way LOCC, and we obtain several efficiently computable upper bounds on the number of secret bits that can be distilled from a bipartite state using one-way LOCC channels; these findings apply not only in the one-shot setting but also in some restricted asymptotic settings. We extend our formalism to private communication over a quantum channel assisted by forward classical communication. We obtain efficiently computable upper bounds on the one-shot forward-assisted private capacity of a channel, thus addressing a question in the theory of quantum-secured communication that has been open for some time now. Our formalism also provides upper bounds on the rate of private communication when using a large number of channels in such a way that the error in the transmitted private data decreases exponentially with the number of channel uses. Moreover, our bounds can be computed using semidefinite programs, thus providing a computationally feasible method to understand the limits of private communication over a quantum network.

中文翻译：

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可扩展性限制量子安全通信和密钥蒸馏

从量子态和通道中蒸馏密钥是量子信息论中感兴趣的中心任务，因为它促进了量子网络上的私有通信。在这里，我们研究了使用本地作和单向经典通信 （one-way LOCC） 从二分态和点对点量子通道进行密钥蒸馏的任务。我们采用不可扩展纠缠的资源理论来研究单向 LOCC 下二分态的变换，我们获得了几个有效可计算的秘密比特数上限，这些秘密比特可以使用单向 LOCC 通道从二分态中提炼出来;这些发现不仅适用于 one-shot 设置，也适用于一些受限的渐近设置。我们将形式主义扩展到通过量子通道进行的私人通信，并辅以前向经典通信。我们获得了通道的一次性前向辅助私有容量的高效可计算上限，从而解决了量子安全通信理论中已经开放了一段时间的问题。我们的形式主义还提供了当使用大量通道时私有通信速率的上限，这样传输的私有数据中的误差会随着通道使用次数呈指数级减少。此外，我们的边界可以使用半定程序进行计算，从而提供了一种计算上可行的方法来理解量子网络上私有通信的限制。