Maximal Privacy Without Coherence

2013/12/31 by Debbie Leung, Ke Li, Graeme Smith +1 · 1 citation
Physics and Astronomy · #quant-ph

paper · pdf · doi:10.1103/physrevlett.113.030502

published as Phys. Rev. Lett. 113, 030502 (2014) · 6 pages. Proof of Eq.(13) slightly revised

arxiv created 2014/02/05 · arxiv updated 2014/07/23

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 d², 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.

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• Maximum privacy without coherence, zero-error

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