Symmetries in quantum key distribution and the connection between optimal attacks and optimal cloning

Agnes Ferenczi and Norbert Lütkenhaus
Phys. Rev. A 85, 052310 – Published 16 May 2012

Abstract

We investigate the connection between the optimal collective eavesdropping attack and the optimal cloning attack where the eavesdropper employs an optimal cloner to attack the quantum key distribution (QKD) protocol. The analysis is done in the context of the security proof in Refs. [Proc. R. Soc. London A 461, 207 (2005); Phys. Rev. Lett. 95, 080501 (2005)] for discrete variable protocols in d-dimensional Hilbert spaces. We consider a scenario in which the protocols and cloners are equipped with symmetries. These symmetries are used to define a quantum cloning scenario. We find that, in general, it does not hold that the optimal attack is an optimal cloner. However, there are classes of protocols, where we can identify an optimal attack by an optimal cloner. We analyze protocols with 2, d and d+1 mutually unbiased bases where d is a prime, and show that for the protocols with 2 and d+1 mutually unbiased bases (MUBs) the optimal attack is an optimal cloner but, for the protocols with d MUBs, it is not. Finally, we give criteria to identify protocols which have different signal states, but the same optimal attack. Using these criteria, we present qubit protocols which have the same optimal attack as the Bennett-Brassard 1984 (BB84) protocol or the 6-state protocol.

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  • Received 26 January 2012

DOI:https://doi.org/10.1103/PhysRevA.85.052310

©2012 American Physical Society

Authors & Affiliations

Agnes Ferenczi* and Norbert Lütkenhaus

  • Institute for Quantum Computing & Department for Physics and Astronomy, University of Waterloo, 200 University Avenue West, N2L 3G1, Waterloo, Ontario, Canada

  • *aferenczi@iqc.ca

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Issue

Vol. 85, Iss. 5 — May 2012

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