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arXiv:quant-ph/0502140 · Physical Review A

Higher-security thresholds for quantum key distribution by improved analysis of dark counts

Jean-Christian Boileau, Jamie Batuwantudawe, Raymond Laflamme

Published Sep 16, 2005• 12 citations
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Abstract

We discuss the potential of quantum key distribution (QKD) for long-distance communication by proposing an analysis of the errors caused by dark counts. We give sufficient conditions for a considerable improvement of the key generation rates and the security thresholds of well-known QKD protocols such as the Bennett-Brassard 1984, Phoenix-Barnett-Chefles 2000, and six-state protocols. This analysis is applicable to other QKD protocols like the Bennett 1992 protocol. We examine two scenarios: a sender using a perfect single-photon source and a sender using a Poissonian source.

DOI
10.1103/physreva.72.032321

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We discuss the potential of quantum key distribution (QKD) for long-distance communication by proposing an analysis of the errors caused by dark counts. We give sufficient conditions for a considerable improvement of the key generation rates and the security thresholds of well-known QKD protocols such as the Bennett-Brassard 1984, Phoenix-Barnett-Chefles 2000, and six-state protocols. This analysis is applicable to other QKD protocols like the Bennett 1992 protocol. We examine two scenarios: a sender using a perfect single-photon source and a sender using a Poissonian source.
We compare the performance of various quantum-key-distribution (QKD) systems using 1550nm up-conversion single-photon detectors. The analysis is based on the error rate and the secure communication rate as a function of distance for three QKD protocols: the Bennett-Brassard 1984, the Beruiett-Brassard-Vlerinin 1992, and the coherent differential-phase-shift keying (DPSK) protocols. We discussed that the security of DPSK protocol against any type of individual photon splitting attack and concluded that the simple and efficient DPSK protocol allows for more than 200km of secure communication distance with high communication rates.
The most important goal of quantum communication is to distribute the encryption key between the transmitter and the receiver. The optimal situation in Quantum Key Distribution (QKD) between transmitter and receiver is to increase the key distribution rate per second, increase the transmission distance, and reduce the error in key distribution. Several protocols used for QKD. The most important of QKD protocols is the BB84. One of the challenges leading to errors in quantum protocols is generating error pulses in single-photon detectors. These pulses caused by the inherent effects of quantum devices. They can cause wrong detection in the receiver. Many measures have been taken in the design and construction of single-photon detectors to reduce this error pulses, but it is not possible to eliminate all of them. Afterpulse and dark counts are two types of unwanted pulses that occur with single-photon detectors. In this paper, a new QKD protocol is proposed. It is an upgrade of the BB84 protocol and can reduce the effects of unwanted pulses such as afterpulse and dark counts in QKD avalanche detectors.
The analysis is based on the error rate and the secure communication rate as functions of distance for three quantum-key-distribution (QKD) protocols: the Bennett–Brassard 1984, the Bennett–Brassard–Mermin 1992, and the coherent differential-phase-shift keying (DPSK) protocols. We consider the secure communication rate of the DPSK protocol against an arbitrary individual attack, including the most commonly considered intercept-resend and photon-number splitting attacks, and concluded that the simple and efficient differential-phase-shift-keying protocol allows for more than 200 km of secure communication distance with high communication rates.
The performance of various quantum-key-distribution (QKD) systems is analyzed using 1.55 μm up-conversion single-photon detector. The dependence of quantum efficiency and dark count rate change on the pump power was also discussed. The comparison is based on the secure communication rate as a function of distance for three QKD protocols: the Bennett-Brassard 1984, the Bennett-Brassard-Mermin 1992, and the coherent differential-phase-shift keying protocols. We show that the up-conversion detector allows for higher communication rate and longer communication distance than the commonly used InGaAs/InP APD for all three QKD protocols, and the properties of quantum key distribution system can be greatly improved by this detector.
Quantum information theory is a modern branch of theoretical physics. One of its main goals is to interpret concepts of quantum physics. This leads to a deeper understanding of quantum theory. The most common examples of practical applications of basic quantum theory are quantum computation and quantum cryptography. Quantum cryptography provides secure communication between legitimate users even in the presence of an adversary by making possible the distribution of a secret key. It then allows error correction and privacy amplification, which is elimination of adversary information, through classical communication. In this thesis two important aspects of quantum key distribution are covered, namely robustness bounds with respect to provable entanglement for ideal protocols and practical quantum key distribution using two-way classical communication. In part one of the thesis, ideal quantum key distribution protocols and their robustness in terms of provable entanglement are discussed. The robustness bounds are proved for most general coherent attacks. These bounds for provable entanglement are already known to be 25% for the four-state protocol and 33% for the six-state protocol. We anticipate to provide a region in which the legitimate users share entanglement. This region is large for the four-state protocol and is reduced to a smaller region for the six-state protocol because of additional constraint on it. We also investigate the information cost which the adversary has to pay in order to reach these bounds. In part two we adopt a more practical approach. We investigate the limitation on distance of secure communication because of practical restrictions. In particular we investigate the restrictions due to the lack of single photon sources, the lossy channel and faulty detectors. These practical limitations have already been observed using one-way classical communication between legitimate users. It has been observed that it is actually the dark count rate that limit the distance up to which legitimate users can share a secret key. We have used two-way classical communication to postpone the effect of dark counts and increase the distance to considerable amount. For the purpose we have considered an optimal attack with respect to the disturbance that an eavesdropper creates while attacking. Any other format of attacking will increase the disturbance. We show that using two-way classical communication for post processing we can increase the distance of secure communication considerably.
Communications in secrecy are often required in many commercial and military applications. Unfortunately, many cryptographic schemes in use today such as public-key cryptography based on the RSA algorithm would be broken with either unanticipated advances in hardware and algorithm or the advent of quantum computers. Quantum cryptography, on the other hand, has been proven secure even against the most general attack allowed by the laws of physics and is a promising technology poised for widespread adoption in realistic cryptographic applications. Quantum cryptography allows two parties to expand on a secret key that they have previously shared. Various quantum cryptographic protocols have been proposed to perform this task. In this paper, we survey some popular quantum cryptographic protocols (including the famous Bennett-Brassard 1984 protocol) and discuss their security. Specifically, we consider their security in two cases: the ideal case where a perfect single-photon source is used and the practical case where a realistic laser source is used. We compare the protocols and find that the efficient six-state protocol outperforms the others both in the tolerable quantum bit error rate and in the key generation rate when a realistic laser source is used.