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arXiv:quant-ph/0702250 · Physical Review A

Upper bounds of eavesdropper’s performances in finite-length code with the decoy method

Masahito Hayashi

Published Jul 26, 2007• 117 citations
arXivHTMLPDF

Abstract

Security formulas of quantum key distribution (QKD) with imperfect resources are obtained for finite-length code when the decoy method is applied. This analysis is useful for guaranteeing the security of implemented QKD systems. Our formulas take into account the effect of the vacuum state and dark counts in the detector. We compare the asymptotic key generation rate in the presence of dark counts to that without the presence of dark counts.

DOI
10.1103/physreva.76.012329

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Dianzi xuebao•Jan 1, 2012•0 citations
Security formulas of quantum key distribution (QKD) with imperfect resources are obtained for finite-length code when the decoy method is applied. This analysis is useful for guaranteeing the security of implemented QKD systems. Our formulas take into account the effect of the vacuum state and dark counts in the detector. We compare the asymptotic key generation rate in the presence of dark counts to that without the presence of dark counts.
Decoy state method quantum key distribution (QKD) is one of the promising practical solutions to BB84 QKD with coherent light pulses. In the real world, however, statistical fluctuations with the finite code length cannot be negligible, and the securities of theoretical and experimental researches of the decoy method state QKD so far are based on the asymptotic GLLP's formula which guarantees only that the limit of eavesdropper's information becomes zero as the code length approaches infinity. In this paper, we propose a substantially improved decoy state QKD in the framework of the finite code length and derive the upper bound of eavesdropper's information in the finite code length decoy state QKD with arbitrary number of decoy states of different intensities incorporating the finite statistics. We also show the performance of our decoy QKD and optimal values of parameters by numerical simulation.
Many papers have proven the security of quantum key distribution (QKD) systems in the asymptotic framework. The degree of the security has not been discussed in the finite coding-length framework, sufficiently. However, to guarantee any implemented QKD system required, it is needed to evaluate a protocol with a finite coding length. For this purpose, we derive a tight upper bound of the eavesdropper's information. This bound is better than existing bounds. We also obtain the exponential rate of the eavesdropper's information. Further, we approximate our bound by using the normal distribution.
The use of decoy states in quantum key distribution (QKD) has provided a method for substantially increasing the secret key rate and distance that can be covered by QKD protocols with practical signals. The security analysis of these schemes, however, leaves open the possibility that the development of better proof techniques or better classical postprocessing methods might further improve their performance in realistic scenarios. In this paper, we derive upper bounds on the secure key rate for decoy-state QKD. These bounds are based basically only on the classical correlations established by the legitimate users during the quantum communication phase of the protocol. The only assumption about the possible postprocessing methods is that double click events are randomly assigned to single click events. Further, we consider only secure key rates based on the uncalibrated device scenario which assigns imperfections such as detection inefficiency to the eavesdropper. Our analysis relies on two preconditions for secure two-way and one-way QKD. The legitimate users need to prove that there exists no separable state (in the case of two-way QKD) or that there exists no quantum state having a symmetric extension (one-way QKD) that is compatible with the available measurements results. Both criteria have been previously applied to evaluate single-photon implementations of QKD. Here we use them to investigate a realistic source of weak coherent pulses. The resulting upper bounds can be formulated as a convex optimization problem known as a semidefinite program which can be efficiently solved. For the standard four-state QKD protocol, they are quite close to known lower bounds, thus showing that there are clear limits to the further improvement of classical postprocessing techniques in decoy-state QKD.
The laws of quantum physics can be used to secure communications between two distant parties in a scheme called quantum key distribution (QKD), even against a technologically unlimited eavesdropper. While the theoretical security of QKD has been proved rigorously, current implementations of QKD are generally insecure. In particular, mathematical models of devices, such as detectors, do not accurately describe their real-life behaviour. Such seemingly insignificant discrepancies can compromise the security of the entire scheme, especially as novel detector technologies are being developed with little regard for potential vulnerabilities.In this thesis, we study how detector imperfections can impact the security of QKD and how to overcome such technological limitations. We first analyze the security of a high-speed QKD system with finite detector dead time tau. We show that the previously reported sifting approaches are not guaranteed to be secure in this regime. More specifically, Eve can induce a basis-dependent detection efficiency at the receiver's end. Modified key sifting schemes that are basis-independent, and thus secure in the presence of dead time and an active eavesdropper, are discussed and compared. It is shown that the maximum key generation rate is 1/(2tau) for passive basis selection, and 1/tau for active basis selection. The security analysis is also extended to the decoy state BB84 protocol.We then study a relatively new type of single-photon detector called the superconducting nanowire single-photon detector (SNSPD), and discover some unexpected behaviour. We report an afterpulsing effect present when the SNSPD is operated in the high bias current regime. In our standard set-up, the afterpulsing is most likely to occur at around 180 ns following a detection event, for both real counts and dark counts. We characterize the afterpulsing behaviour and speculate that it is not due to the SNSPD itself but rather the associated read-out circuit. We also report and examine a short-lived enhancement of detection efficiency during the recovery of the SNSPD, as well as a longer dead time than previously thought. These findings should be of interest not only to the QKD community but also researchers using SNSPDs in other applications.
This paper proposes models for analyzing the security of decoy-state quantum key distribution(QKD) with state-dependent imperfections.With the privacy amplification method of QKD's post-processing techniques,we introduce the decoy-state method used widely in QKD system to estimate the phase error rate more accurately than the case without decoy-state method.Based on this,we obtain the formula of secret key generation rates for decoy-state QKD with state-dependent imperfections,and characterize the relationship among key generation rates,state dependent parameter,detection efficiency and transmission distance.Numerical simulations indicate that the secure key generation rates' tolerance to state-dependent imperfections decreases with the growing distance,but increases with the improving detection efficiency,which,to some extent,show the validity of the formula we obtain.