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arXiv:1009.1047 · Quantum Information and Computation

Security of quantum key distribution with state-dependent imperfections

Hong-Wei Li, Zhen−Qiang Yin, Shuang Wang, Wan‐Su Bao, Guang‐Can Guo, Zheng‐Fu Han

Published Nov 1, 2011• 3 citations
arXivHTMLPDF

Abstract

In practical quantum key distribution system, the state preparation and measurement have state-dependent imperfections comparing with the ideal BB84 protocol. If the state-dependent imperfection can not be regarded as an unitary transformation, it should not be considered as part of quantum channel noise introduced by the eavesdropper, the commonly used secret key rate formula GLLP can not be applied correspondingly. In this paper, the unconditional security of quantum key distribution with state-dependent imperfections will be analyzed by estimating upper bound of the phase error rate in the quantum channel and the imperfect measurement. Interestingly, since Eve can not control all phase error in the quantum key distribution system, the final secret key rate under constant quantum bit error rate can be improved comparing with the perfect quantum key distribution protocol.

DOI
10.26421/qic11.11-12-4

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Dianzi xuebao•Jan 1, 2012•0 citations
In practical quantum key distribution system, the state preparation and measurement have state-dependent imperfections comparing with the ideal BB84 protocol. If the state-dependent imperfection can not be regarded as an unitary transformation, it should not be considered as part of quantum channel noise introduced by the eavesdropper, the commonly used secret key rate formula GLLP can not be applied correspondingly. In this paper, the unconditional security of quantum key distribution with state-dependent imperfections will be analyzed by estimating upper bound of the phase error rate in the quantum channel and the imperfect measurement. Interestingly, since Eve can not control all phase error in the quantum key distribution system, the final secret key rate under constant quantum bit error rate can be improved comparing with the perfect quantum key distribution protocol.
The security of the perfect quantum key distribution protocol can be guaranteed by applying the fundamental laws of quantum mechanics, but the practical quantum key distribution system may be attacked by utilizing imperfect state preparation and measurement devices. In this work, we analyze the security of the practical quantum key distribution system with weak-randomness basis selection, where the basis selection may be partly controlled by the eavesdropper due to the imperfect quantum devices. We propose the parameter $\ensuremath{\epsilon}$ to quantify the deviation value between the practical basis selection probability and the perfect basis selection probability, and the secret key rate of the practical quantum key distribution system is obtained under different $\ensuremath{\epsilon}$ values. By applying the practical experimental parameters, the analysis result demonstrates that the maximal transmission distance will be reduced from 142 to 139 km if $\ensuremath{\epsilon}\ensuremath{\le}0.1$, but no secret key can be generated in the case of $\ensuremath{\epsilon}\ensuremath{\ge}0.34$.
The ideal quantum key distribution (QKD) protocol requires perfect random numbers for bit encoding and basis selecting. Perfect randomness is of great significance to the practical QKD system. However, due to the imperfection of practical quantum devices, an eavesdropper (Eve) may acquire some random numbers, thus affecting the security of practical systems. In this paper, we analyze the effects of the weak randomness in the measurement-device-independent QKD (MDI-QKD) with finite resources. We analytically derive concise formulas for estimating the lower bound of the single-photon yield and the upper bound of the phase error rate in the case of the weak randomness. The simulation demonstrates that the final secret key rate of MDI-QKD with finite resources is sensitive to state preparation, even with a small proportion of weak randomness, the secure key rate has a noticeable fluctuation. Therefore, the weak randomness of the state preparation may bring additional security risks. In order to ensure the practical security of the QKD system, we are supposed to strengthen the protection of state preparation devices.
For the past few years, the security of practical quantum key distribution systems has attracted a lot of attention. Device-independent quantum key distribution was proposed to design a real-life secure quantum key distribution system with imperfect and untrusted quantum devices. In this paper, we analyzed the security of BB84 protocol in a device-independent scenario based on the entanglement distillation method. Since most of the reported loopholes are in receivers of quantum key distribution systems, we focus on condition that the transmitter of the system is perfectly coincident with the requirement of the BB84 protocol, while the receiver can be controlled by eavesdropper. Finally, the lower bound of the final secret-key rate was proposed and we explained why the secure-key rate is similar to the well-known result for the original entanglement distillation protocol.
Standard security proofs of quantum-key-distribution (QKD) protocols often rely on symmetry arguments. In this paper, we prove the security of a three-state protocol that does not possess rotational symmetry. The three-state QKD protocol we consider involves three qubit states, where the first two states $\ensuremath{\mid}{0}_{z}⟩$ and $\ensuremath{\mid}{1}_{z}⟩$ can contribute to key generation, and the third state $\ensuremath{\mid}+⟩=(\ensuremath{\mid}{0}_{z}⟩+\ensuremath{\mid}{1}_{z}⟩)∕\sqrt{2}$ is for channel estimation. This protocol has been proposed and implemented experimentally in some frequency-based QKD systems where the three states can be prepared easily. Thus, by founding on the security of this three-state protocol, we prove that these QKD schemes are, in fact, unconditionally secure against any attacks allowed by quantum mechanics. The main task in our proof is to upper bound the phase error rate of the qubits given the bit error rates observed. Unconditional security can then be proved not only for the ideal case of a single-photon source and perfect detectors, but also for the realistic case of a phase-randomized weak coherent light source and imperfect threshold detectors. Our result in the phase error rate upper bound is independent of the loss in the channel. Also, we compare the three-state protocol with the Bennett-Brassard 1984 (BB84) protocol. For the single-photon source case, our result proves that the BB84 protocol strictly tolerates a higher quantum bit error rate than the three-state protocol, while for the coherent-source case, the BB84 protocol achieves a higher key generation rate and secure distance than the three-state protocol when a decoy-state method is used.
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.