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arXiv:quant-ph/0311066 · Physical Review A

Effect of finite detector efficiencies on the security evaluation of quantum key distribution

Marcos Curty, Norbert Lütkenhaus

Published Apr 28, 2004• 27 citations
arXivHTMLPDF

Abstract

Quantum key distribution with the Bennett-Brassard 1984 protocol has been shown to be unconditionally secure even using weak coherent pulses instead of single-photon signals. The distances that can be covered by these methods are limited due to the loss in the quantum channel (e.g., loss in the optical fiber) and in the single-photon counters of the receivers. One can argue that the loss in the detectors cannot be changed by an eavesdropper in order to increase the covered distance. Here we show that the security analysis of this scenario is not as easy as is commonly assumed, since already two-photon processes allow eavesdropping strategies that outperform the known photon-number splitting attack. For this reason there is, so far, no satisfactory security analysis available in the framework of individual attacks.

DOI
10.1103/physreva.69.042321

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Quantum key distribution with the Bennett-Brassard 1984 protocol has been shown to be unconditionally secure even using weak coherent pulses instead of single-photon signals. The distances that can be covered by these methods are limited due to the loss in the quantum channel (e.g., loss in the optical fiber) and in the single-photon counters of the receivers. One can argue that the loss in the detectors cannot be changed by an eavesdropper in order to increase the covered distance. Here we show that the security analysis of this scenario is not as easy as is commonly assumed, since already two-photon processes allow eavesdropping strategies that outperform the known photon-number splitting attack. For this reason there is, so far, no satisfactory security analysis available in the framework of individual attacks.
We investigate the security of quantum key distribution with entangled photons, focusing on the two-photon variation of the Bennett-Brassard 1984 (BB84) protocol proposed in 1992 by Bennett, Brasard, and Mermin (BBM92). We present a proof of security which applies to realistic sources, and to untrustable sources which can be placed outside the labs of the two receivers. The proof is restricted to individual eavesdropping attacks, and assumes that the detection apparatus is trustable. We find that the average collision probability for the BBM92 protocol is the same as that of the BB84 protocol with an ideal single-photon source. This indicates that there is no analog in BBM92 to photon splitting attacks, and that the source can be placed between the two receivers without changing the form of the collision probability. We then compare the communication rate of both protocols as a function of distance, and show that BBM92 has potential for much longer communication distances, up to 170 km, in the presence of realistic experimental imperfections. Finally, we propose a scheme based on entanglement swapping that can lead to even longer distance communication. The limiting factor in this scheme is the channel loss, which imposes very slow communication rates at longer distances.
Unconditional security proofs of the Bennett-Brassard 1984 protocol of quantum key distribution have been obtained recently. These proofs cover also practical implementations that utilize weak coherent pulses in the four signal polarizations. Proven secure rates leave open the possibility that new proofs or new public discussion protocols will obtain larger rates over increased distance. In this paper we investigate limits to the error rate and signal losses that can be tolerated by future protocols and proofs.
Abstract The single-photon detectionefficiency of the detector unit is crucial for the security of common quantum key distribution protocols like Bennett-Brassard 1984 (BB84). A low value for the efficiency indicates a possible eavesdropping attack that exploits the photon receiver’s imperfections. We present a method for estimating the detection efficiency, and calculate the corresponding secure key generation rate. The estimation is done by testing gated detectors using a randomly activated photon source inside the receiver unit. This estimate gives a secure rate for any detector with non-unity single-photon detection efficiency, both inherit or due to blinding. By adding extra optical components to the receiver, we make sure that the key is extracted from photon states for which our estimate is valid. The result is a quantum key distribution scheme that is secure against any attack that exploits detector imperfections.
We report the security analysis of time-coding quantum key distribution protocols. The protocols make use of coherent single-photon pulses. The key is encoded in the photon time-detection. The use of coherent superposition of states allows to detect eavesdropping of the key. We give a mathematical model of a first protocol from which we derive a second, simpler, protocol. We derive the security analysis of both protocols and find that the secure rates can be similar to those obtained with the BB84 protocol. We then calculate the secure distance for those protocols over standard fibre links. When using low-noise superconducting single photon detectors, secure distances over 200 km can be foreseen. Finally, we analyse the consequences of photon-number splitting attacks when faint pulses are used instead of single photon pulses. A decoy states technique can be used to prevent such attacks.
We report the security analysis of time-coding quantum key distribution protocols. The protocols make use of coherent single-photon pulses. The key is encoded in the photon time-detection. The use of coherent superposition of states allows to detect eavesdropping of the key. We give a mathematical model of a first protocol from which we derive a second, simpler, protocol. We derive the security analysis of both protocols and find that the secure rates can be similar to those obtained with the BB84 protocol. We then calculate the secure distance for those protocols over standard fibre links. When using low-noise superconducting single photon detectors, secure distances over 200 km can be foreseen. Finally, we analyse the consequences of photon-number splitting attacks when faint pulses are used instead of single photon pulses. A decoy states technique can be used to prevent such attacks.
Quantum key distribution can be performed with practical signal sources such as weak coherent pulses. One example of such a scheme is the Bennett-Brassard protocol that can be implemented via polarization of the signals, or equivalent signals. It turns out that the most powerful tool at the disposition of an eavesdropper is the photon-number splitting attack. We show that this attack can be extended in the relevant parameter regime so as to preserve the Poissonian photon number distribution of the combination of the signal source and the lossy channel.