Maximal privacy without coherence

Abstract

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 Nd with input dimension d2, quantum capacity Q(Nd)≤1, and private capacity P(Nd)=logd. These channels asymptotically saturate an interesting inequality P(N)≤(1/2)[logdA+Q(N)] for any channel N with input dimension dA and capture the essence of privacy stripped of the confounding influence of coherence. © 2014 American Physical Society.