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.

翻译：从量子态和量子信道中提取秘密密钥是量子信息理论的核心任务，因为它促进了量子网络上的私密通信。本文研究利用局域操作和单向经典通信（单向LOCC）从二分态和点对点量子信道中提取秘密密钥的任务。我们采用不可扩展纠缠的资源理论来研究二分态在单向LOCC下的转化，并获得了多个可高效计算的上界，这些上界限制了通过单向LOCC信道从二分态中可提取的秘密比特数；这些结果不仅适用于单次设置，也适用于某些受限的渐近设置。我们将该形式体系扩展到由前向经典通信辅助的量子信道私密通信。我们获得了信道单次前向辅助私密容量的可高效计算上界，从而解决了量子安全通信理论中长期悬而未决的问题。我们的形式体系还为使用大量信道时私密通信的速率提供了上界，此时传输私密数据的误差随信道使用次数呈指数下降。此外，我们的上界可通过半定规划计算，从而为理解量子网络上私密通信的极限提供了一种计算可行的方法。