"Pretty strong" converse for the private capacity of degraded quantum wiretap channels

TL;DR

This paper establishes a pretty strong converse for the private capacity of degraded classical-quantum-quantum wiretap channels, extending the understanding of privacy limits in quantum communication with some remaining gaps.

Contribution

It adapts techniques from quantum information theory to prove a pretty strong converse for the private capacity of degraded cqq-wiretap channels, generalizing classical results.

Findings

Proves a pretty strong converse for degraded cqq-wiretap channels.

Identifies a gap between error and privacy parameters where the bound applies.

Advances understanding of strong converses in quantum wiretap channel capacities.

Abstract

In the vein of the recent "pretty strong" converse for the quantum and private capacity of degradable quantum channels [Morgan/Winter, IEEE Trans. Inf. Theory 60(1):317-333, 2014], we use the same techniques, in particular the calculus of min-entropies, to show a pretty strong converse for the private capacity of degraded classical-quantum-quantum (cqq-)wiretap channels, which generalize Wyner's model of the degraded classical wiretap channel. While the result is not completely tight, leaving some gap between the region of error and privacy parameters for which the converse bound holds, and a larger no-go region, it represents a further step towards an understanding of strong converses of wiretap channels [cf. Hayashi/Tyagi/Watanabe, arXiv:1410.0443 for the classical case].