arXiv:1312.4989 · Physical Review Letters

Maximal Privacy without Coherence

Debbie Leung, Ke Li, Graeme Smith, John A. Smolin

Published Jul 16, 2014• 19 citations

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 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.

DOI: 10.1103/physrevlett.113.030502

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