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 ${\mathcal{N}}_d$ with input dimension $d^2$, quantum capacity $Q({\mathcal{N}}_d)\le 1$, and private capacity $P({\mathcal{N}}_d)=\log d$. These channels asymptotically saturate an interesting inequality $P(\mathcal{N})\le (1/2)[\log d_A+Q(\mathcal{N})]$ for any channel $\mathcal{N}$ with input dimension $d_A$ and capture the essence of privacy stripped of the confounding influence of coherence.

• Received 7 February 2014

DOI:https://doi.org/10.1103/PhysRevLett.113.030502