Extendibility limits quantum-secured communication and key distillation

• URL: http://arxiv.org/abs/2410.21393v1
• Date: Mon, 28 Oct 2024 18:00:11 GMT
• Title: Extendibility limits quantum-secured communication and key distillation
• Authors: Vishal Singh, Mark M. Wilde,
• Abstract summary: We study the task of secret-key distillation from bipartite states and point-to-point quantum channels. We extend our formalism to private communication over a quantum channel assisted by forward classical communication.
• Score: 4.079147243688764
• License:
• Abstract: 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.

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