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Kluwer Academic Publishers eBooks

Quantum Key Distribution Using Multilevel Encoding

Mohamed Bourennane, Anders Karlsson, Gunnar G. Bjork

Published Feb 24, 2006• 5 citations
Publisher

Abstract

We extend the original Bennett and Brassard for quantum key distribution protocol by using M mutually complementary bases and N orthogonalvectors in each base. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
DOI
10.1007/0-306-47114-0_46

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In this article, protocols for quantum key distribution based on encoding in higher dimensional systems in N-dimensional Hilbert space are proposed. We extend the original Bennett-Brassard protocol using two complementary bases and two-dimensional states to M mutually complementary bases and N orthogonal vectors in each base. We study the mutual information between the legitimate parties and the eavesdropper and the error rate by considering various incoherent eavesdropping attacks as a function of the dimension of the Hilbert space.
We propose secure protocols for user authenticated quantum key distribution. We argue that the use of a trusted authority becomes inevitable in a realistic environment as that of multi-user key distribution. Here, we specifically look at one protocol that use nonorthogonal bases with two-qubit entanglement. As the trusted authority being the only one knowing the correlations of this entanglement he/she can protect an unauthorized user from getting the right key. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
An experimental free-space quantum key distribution (QKD) system has been tested over an outdoor optical path of ~ 1 km under nighttime conditions at Los Alamos National Laboratory. This system employs the Bennett 92 protocol; here we give a brief overview of this protocol, and describe our experimental implementation of it. An analysis of the system efficiency is presented, as well as a description of our error detection protocol, which employs a two-dimensional parity check scheme. Finally, the susceptibility of this system to eavesdropping by various techniques is determined. Possible applications include the rekeying of satellites in low earth orbit. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
Recall that in the Bennett–Brassard key distribution scheme, after Alice and Bob have obtained bit strings that ideally are supposed to be identical, they have to do some further processing to make sure they end up with strings that really are identical. Our first goal in this chapter is to show how they can do this. As you might expect, we will use error-correcting codes of the sort we have been discussing in the preceding chapter. However, the way we use error-correcting codes in quantum key distribution is not quite the same as in classical communication. Normally, one corrects errors by encoding one's message into special codewords that are sufficiently different from each other that they will still be distinguishable after passing through a noisy channel. But in quantum key distribution the “noise” of the channel might actually be the effect of an eavesdropper who is free to manipulate the signals sent by Alice. Ordinary error correction is not designed for such a setting. So instead of using codewords to encode the original transmission, we wait until all the bits have been sent and then use an error-correcting code after the fact . In this respect error correction in quantum key distribution is similar to the use of an error-correcting code in the “hat problem” discussed at the end of Chapter 4. There also, the error-correcting code is applied only after all the data – in that case the vector of hat colors – has been generated and conveyed to the participants.