Maximal Privacy Without Coherence
Abstract
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 Q(N_d) <= 1, and private capacity P(N_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.
Cite
@article{arxiv.1312.4989,
title = {Maximal Privacy Without Coherence},
author = {Debbie Leung and Ke Li and Graeme Smith and John Smolin},
journal= {arXiv preprint arXiv:1312.4989},
year = {2014}
}
Comments
6 pages. Proof of Eq.(13) slightly revised