Public and private resource trade-offs for a quantum channel

Public and private resource trade-offs for a quantum channel 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Quantum Information Processing Springer Journals

Public and private resource trade-offs for a quantum channel

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Publisher
Springer Journals
Copyright
Copyright © 2011 by Springer Science+Business Media, LLC
Subject
Physics; Quantum Information Technology, Spintronics; Quantum Computing; Data Structures, Cryptology and Information Theory; Quantum Physics; Mathematical Physics
ISSN
1570-0755
eISSN
1573-1332
D.O.I.
10.1007/s11128-011-0317-z
Publisher site
See Article on Publisher Site

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.

Journal

Quantum Information ProcessingSpringer Journals

Published: Oct 18, 2011

References

  • Conjugate degradability and the quantum capacity of cloning channels
    Brádler, K.; Dutil, N.; Hayden, P.; Muhammad, A.
  • Entanglement breaking channels
    Horodecki, M.; Shor, P.W.; Ruskai, M.B.
  • Entanglement-assisted capacity of quantum multiple-access channels
    Hsieh, M.H.; Devetak, I.; Winter, A.
  • Trading classical communication, quantum communication, and entanglement in quantum Shannon theory
    Hsieh, M.H.; Wilde, M.M.
  • Entanglement-assisted communication of classical and quantum information
    Hsieh, M.H.; Wilde, M.M.

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