Upper bounds for the secure key rate of the decoy-state quantum key distribution

Marcos Curty, Tobias Moroder, Xiongfeng Ma, Hoi-Kwong Lo, and Norbert Lütkenhaus
Phys. Rev. A 79, 032335 – Published 26 March 2009

Abstract

The use of decoy states in quantum key distribution (QKD) has provided a method for substantially increasing the secret key rate and distance that can be covered by QKD protocols with practical signals. The security analysis of these schemes, however, leaves open the possibility that the development of better proof techniques or better classical postprocessing methods might further improve their performance in realistic scenarios. In this paper, we derive upper bounds on the secure key rate for decoy-state QKD. These bounds are based basically only on the classical correlations established by the legitimate users during the quantum communication phase of the protocol. The only assumption about the possible postprocessing methods is that double click events are randomly assigned to single click events. Further, we consider only secure key rates based on the uncalibrated device scenario which assigns imperfections such as detection inefficiency to the eavesdropper. Our analysis relies on two preconditions for secure two-way and one-way QKD. The legitimate users need to prove that there exists no separable state (in the case of two-way QKD) or that there exists no quantum state having a symmetric extension (one-way QKD) that is compatible with the available measurements results. Both criteria have been previously applied to evaluate single-photon implementations of QKD. Here we use them to investigate a realistic source of weak coherent pulses. The resulting upper bounds can be formulated as a convex optimization problem known as a semidefinite program which can be efficiently solved. For the standard four-state QKD protocol, they are quite close to known lower bounds, thus showing that there are clear limits to the further improvement of classical postprocessing techniques in decoy-state QKD.

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  • Received 29 January 2009

DOI:https://doi.org/10.1103/PhysRevA.79.032335

©2009 American Physical Society

Authors & Affiliations

Marcos Curty1, Tobias Moroder2,3, Xiongfeng Ma2, Hoi-Kwong Lo4, and Norbert Lütkenhaus2,3

  • 1Department of Signal Theory and Communications, ETSI Telecomunicación, University of Vigo, Campus Universitario, E-36310 Vigo (Pontevedra), Spain
  • 2Institute for Quantum Computing, University of Waterloo, Waterloo, Ontario, Canada N2L 3G1
  • 3Quantum Information Theory Group, Institut für Theoretische Physik I, and Max-Planck Research Group, Institute of Optics, Information and Photonics, University of Erlangen–Nürnberg, 91058 Erlangen, Germany
  • 4Department of Electrical and Computer Engineering and Department of Physics, Center for Quantum Information and Quantum Control (CQIQC), University of Toronto, Toronto, Ontario, Canada M5S 3G4

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Vol. 79, Iss. 3 — March 2009

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