The private classical capacity with a symmetric side channel and its application to quantum cryptography

TL;DR

This paper derives a single-letter formula for the symmetric-side-channel-assisted private capacity of quantum channels, showing its properties and implications for quantum cryptography, especially in quantum key distribution protocols.

Contribution

It introduces a new formula for the symmetric-side-channel-assisted private capacity and explores its properties, including additivity and convexity, with applications to quantum cryptography.

Findings

Capacity is additive and convex.

For degradable channels, assisted and unassisted capacities are equal.

Collective attacks are stronger than individual attacks in BB84.

Abstract

We study the symmetric-side-channel-assisted private capacity of a quantum channel, for which we provide a single-letter formula. This capacity is additive, convex, and, for degradable channels, equal to the unassisted private capacity. While a channel's (unassisted) capacity for for private classical communication may be strictly larger than its quantum capacity, we will show that these capacities are equal for degradable channels, thus demonstrating the equivalence of privacy and quantum coherence in this context. We use these ideas to find new bounds on the key rate of quantum key distribution protocols with one-way classical post-processing. For the Bennett-Brassard-84 (BB84) protocol, our results demonstrate that collective attacks are strictly stronger than individual attacks.