Maximum privacy without coherence, zero-error

TL;DR

This paper investigates the disparity between quantum and private capacities of certain quantum channels in zero-error scenarios, revealing channels with zero quantum capacity but maximum private capacity.

Contribution

It demonstrates an extreme case where zero-error quantum capacity is zero while private capacity reaches its maximum for a specific family of channels.

Findings

Zero-error quantum capacity can be zero.

Zero-error private capacity can be maximal.

Significant difference between quantum and private capacities in zero-error setting.

Abstract

We study the possible difference between the quantum and the private capacities of a quantum channel in the zero-error setting. For a family of channels introduced by arXiv:1312.4989, we demonstrate an extreme difference: the zero-error quantum capacity is zero, whereas the zero-error private capacity is maximum given the quantum output dimension.