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Journal of Physics A Mathematical and Theoretical

A necessary condition for the security of differential-phase-shift quantum key distribution

Adriana Marais, Thomas Konrad, Francesco Petruccione

Published Jun 24, 2010• 3 citations
Publisher

Abstract

A necessary condition for the security of a quantum key distribution protocol is that Bob's measurement is described by non-commuting POVM elements. The differential-phase-shift quantum key distribution protocol is formalised, and this condition is shown to be met.
DOI
10.1088/1751-8113/43/30/305302

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The coherent-one-way and the differential-phase-shift protocols ar e two of the most recent practical quantum key distribution protocols for quantum cryptography. These protocols belong to a class of so-called distributed-phase-reference quantum key distribution protocols. While security proofs for some limited attacks exis t, the unconditional security proofs this class of protocol remain unrealised. The existing tools for proving security of protocols ag ainst the most general attacks fail to apply to this class of protocol in a straight forward way. One of the necessary conditions for a quantum key distribution protocol to be secure is the presence of noncommuting measurements. In this paper, the coherent-one-way protocol is formalised, and we describe Bob's measurements by non-commuting POVM elements, showing that this security condition is met.
The differential phase shift quantum key distribution protocol reveals good security against such powerful attacks as unambiguous state discrimination and beam splitting attacks. Its complete security analysis is complex due to high dimensions of the supposed spaces and density operators. In this paper, we consider a particular and conceptually simple coherent attack, available in practical implementations. The main condition for this attack is the length of used coherent state tuples of order 8–12. We show that under this condition, no high level of practical distance between legitimate users can be achieved.
Differential phase shift quantum key distribution systems have a high potential for achieving high speed key generation. However, its unconditional security proof is still missing, even though it has been proposed for many years. Here, we prove its security against collective attacks with a weak coherent light source in the noiseless case (i.e., no bit error). The only assumptions are that quantum theory is correct, the devices are perfect and trusted and the key size is infinite. Our proof works on threshold detectors. We compute the lower bound of the secret key generation rate using the information-theoretical security proof method. Our final result shows that the lower bound of the secret key generation rate per pulse is linearly proportional to the channel transmission probability if Bob's detection counts obey the binomial distribution.
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Differential-phase-shift quantum key distribution based on two nonorthogonal states is described. A weak coherent pulse train is sent from Alice to Bob, in which the phase of each pulse is randomly modulated by ${0,\ensuremath{\pi}}.$ Bob measures the differential phase by a one-bit delay circuit. The system has a simple configuration without the need for an interferometer and a bright reference pulse in Alice's site, unlike the conventional QKD system based on two nonorthogonal states, and has an advantage of improved communication efficiency. The principle of the operation is successfully demonstrated in experiments.