Maximal Privacy without Coherence

Privacy is a fundamental feature 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 Q(N-d) <= 1, and private capacity P(N-d) = log d. These channels asymptotically saturate an interesting inequality P(N) <= (1/2) [log d(A) + Q(N)] for any channel N with input dimension d(A) and capture the essence of privacy stripped of the confounding influence of coherence.