Maximal Privacy Without Coherence

Privacy lies at the fundament of quantum mechanics. A coherently transmitted quantum state is inherently private. Remarkably, coherent quantum communication is not a prerequisite for privacy: there are quantum channels that are too noisy to transmit any quantum information reliably that can nevertheless send private classical information. Here, we ask how much private classical information a channel can transmit if it has little quantum capacity. We present a class of channels N_d with input dimension d^2, quantum capacity QN_d <= 1, and private capacity PN_d = log d. These channels asymptotically saturate an interesting inequality P(N) <= log d_A + Q(N)/2 for any channel N with input dimension d_A, and capture the essence of privacy stripped of the confounding influence of coherence.