Limiting one-way distillable secret key via privacy testing of extendible states

Vishal Singh; Karol Horodecki; Aby Philip; Mark M. Wilde

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arXiv · 2511.04438

Limiting one-way distillable secret key via privacy testing of extendible states

Vishal Singh·Karol Horodecki·Aby Philip·Mark M. Wilde

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Abstract

The notions of privacy tests and $k$-extendible states have both been instrumental in quantum information theory, particularly in understanding the limits of secure communication. In this paper, we determine the maximum probability with which an arbitrary $k$-extendible state can pass a privacy test, and we prove that it is equal to the maximum fidelity between an arbitrary $k$-extendible state and the standard maximally entangled state. Our findings, coupled with the resource theory of $k$-unextendibility, lead to an efficiently computable upper bound on the one-shot, one-way distillable key of a bipartite state, and we prove that it is equal to the best-known efficiently computable upper bound on the one-shot, one-way distillable entanglement. We also establish efficiently computable upper bounds on the one-shot, forward-assisted private capacity of channels. Extending our formalism to the independent and identically distributed setting, we obtain single-letter efficiently computable bounds on the $n$-shot, one-way distillable key of a state and the $n$-shot, forward-assisted private capacity of a channel. For some key examples of interest, our bounds are significantly tighter than other known efficiently computable bounds.

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Vishal Singh, Karol Horodecki, Aby Philip, Mark M. Wilde. 2025-11-06. Limiting one-way distillable secret key via privacy testing of extendible states. https://arxiv.org/abs/2511.04438

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