Can non-private channels transmit quantum information?

TL;DR

This paper investigates quantum channels with minimal private capacity and reveals that, when combined, they can transmit significantly more quantum information than expected, challenging additivity assumptions.

Contribution

It provides evidence that certain pairs of low-private-capacity channels can jointly transmit much more quantum information, demonstrating large violations of additivity.

Findings

Channels with small private capacity can jointly transmit large quantum information

Strong violations of additivity for private capacity and Holevo information are demonstrated

Implications for understanding quantum communication limits and capacities

Abstract

We study the power of quantum channels with little or no capacity for private communication. Because privacy is a necessary condition for quantum communication, one might expect that such channels would be of little use for transmitting quantum states. Nevertheless, we find strong evidence that there are pairs of such channels that, when used together, can transmit far more quantum information than the sum of their individual private capacities. Because quantum transmissions are necessarily private, this would imply a large violation of additivity for the private capacity. Specifically, we present channels which display either (1) A large joint quantum capacity but very small individual private capacities or (2) a severe violation of additivity for the Holevo information.