Postselection Technique for Quantum Channels with Applications to Quantum Cryptography

Matthias Christandl, Robert König, and Renato Renner
Phys. Rev. Lett. 102, 020504 – Published 14 January 2009

Abstract

We propose a general method for studying properties of quantum channels acting on an n-partite system, whose action is invariant under permutations of the subsystems. Our main result is that, in order to prove that a certain property holds for an arbitrary input, it is sufficient to consider the case where the input is a particular de Finetti-type state, i.e., a state which consists of n identical and independent copies of an (unknown) state on a single subsystem. Our technique can be applied to the analysis of information-theoretic problems. For example, in quantum cryptography, we get a simple proof for the fact that security of a discrete-variable quantum key distribution protocol against collective attacks implies security of the protocol against the most general attacks. The resulting security bounds are tighter than previously known bounds obtained with help of the exponential de Finetti theorem.

  • Received 17 September 2008

DOI:https://doi.org/10.1103/PhysRevLett.102.020504

©2009 American Physical Society

Authors & Affiliations

Matthias Christandl

  • Faculty of Physics, Ludwig-Maximilians-Universität München, Theresienstrasse 37, 80333 Munich, Germany

Robert König

  • Institute for Quantum Information, California Institute of Technology, Pasadena, California 91125, USA

Renato Renner

  • Institute for Theoretical Physics, ETH Zurich, 8093 Zurich, Switzerland

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Vol. 102, Iss. 2 — 16 January 2009

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