title: 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 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.
authors.affiliation: Institute for Quantum Computing, University of Waterloo, Waterloo N2L 3G1, Ontario, Canada.
authors.forename: Debbie
authors.initials: D
authors.lastname: Leung
authors.affiliation: IBM T. J. Watson Research Center, Yorktown Heights, New York 10598, USA and Center for Theoretic Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA.
authors.forename: Ke
authors.initials: K
authors.lastname: Li
authors.affiliation: IBM T. J. Watson Research Center, Yorktown Heights, New York 10598, USA.
authors.forename: Graeme
authors.initials: G
authors.lastname: Smith
authors.affiliation: IBM T. J. Watson Research Center, Yorktown Heights, New York 10598, USA.
authors.forename: John A
authors.initials: JA
authors.lastname: Smolin