  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.
