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Public and private resource trade-offs for a quantum channel

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An Erratum to this article was published on 07 August 2012

Abstract

Collins and Popescu realized a powerful analogy between several resources in classical and quantum information theory. The Collins–Popescu analogy states that public classical communication, private classical communication, and secret key interact with one another somewhat similarly to the way that classical communication, quantum communication, and entanglement interact. This paper discusses the information-theoretic treatment of this analogy for the case of noisy quantum channels. We determine a capacity region for a quantum channel interacting with the noiseless resources of public classical communication, private classical communication, and secret key. We then compare this region with the classical-quantum-entanglement region from our prior efforts and explicitly observe the information-theoretic consequences of the strong correlations in entanglement and the lack of a super-dense coding protocol in the public-private-secret-key setting. The region simplifies for several realistic, physically-motivated channels such as entanglement-breaking channels, Hadamard channels, and quantum erasure channels, and we are able to compute and plot the region for several examples of these channels.

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Author notes

  1. Min-Hsiu Hsieh

    Present address: Statistical Laboratory, University of Cambridge, Wilberforce Road, Cambridge, CB3 0WB, UK

Authors and Affiliations

  1. School of Computer Science, McGill University, Montreal, QC, H3A 2A7, Canada

    Mark M. Wilde

  2. ERATO-SORST Quantum Computation and Information Project, Japan Science and Technology Agency, 5-28-3, Hongo, Bunkyo-ku, Tokyo, Japan

    Min-Hsiu Hsieh

Authors
  1. Mark M. Wilde
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  2. Min-Hsiu Hsieh
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Correspondence to Mark M. Wilde.

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Wilde, M.M., Hsieh, MH. Public and private resource trade-offs for a quantum channel. Quantum Inf Process 11, 1465–1501 (2012). https://doi.org/10.1007/s11128-011-0317-z

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  • DOI: https://doi.org/10.1007/s11128-011-0317-z

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