Extendibility limits quantum-secured communication and key distillation

TL;DR

This paper establishes fundamental limits on quantum-secured communication and key distillation using resource theory, providing computable bounds on secret key rates and private capacities for quantum states and channels.

Contribution

It introduces a resource-theoretic framework to derive efficiently computable upper bounds on secret key distillation and private capacity in quantum networks, addressing open questions in quantum communication.

Findings

Derived upper bounds on secret bits from bipartite states using one-way LOCC.

Established bounds on one-shot forward-assisted private capacity of quantum channels.

Provided semidefinite programming methods for computing private communication limits.

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.