Complementarity of private and correctable subsystems in quantum cryptography and error correction

Dennis Kretschmann, David W. Kribs, and Robert W. Spekkens
Phys. Rev. A 78, 032330 – Published 24 September 2008

Abstract

We make an explicit connection between fundamental notions in quantum cryptography and quantum error correction. Error-correcting subsystems (and subspaces) for quantum channels are the key vehicles for contending with noise in physical implementations of quantum information processing. Private subsystems (and subspaces) for quantum channels play a central role in cryptographic schemes such as quantum secret sharing and private quantum communication. We show that a subsystem is private for a channel precisely when it is correctable for a complementary channel. This result is shown to hold even for approximate notions of private and correctable defined in terms of the diamond norm for superoperators.

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  • Received 21 November 2007

DOI:https://doi.org/10.1103/PhysRevA.78.032330

©2008 American Physical Society

Authors & Affiliations

Dennis Kretschmann1,2, David W. Kribs3,4, and Robert W. Spekkens5

  • 1Institut für Mathematische Physik, Technische Universität Braunschweig, Mendelssohnstraße 3, 38106 Braunschweig, Germany
  • 2Quantum Information Theory Group, Dipartimento di Fisica A. Volta, Università di Pavia, via Bassi 6, 27100 Pavia, Italy
  • 3Department of Mathematics and Statistics, University of Guelph, Guelph, ON, Canada N1G 2W1
  • 4Institute for Quantum Computing, University of Waterloo, ON, Canada N2L 3G1
  • 5Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Cambridge CB3 0WA, United Kingdom

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Issue

Vol. 78, Iss. 3 — September 2008

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