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arXiv:quant-ph/0503005 · Physical Review A

Practical decoy state for quantum key distribution

Xiongfeng Ma, Bing Qi, Yi Bing Zhao, Hoi‐Kwong Lo

Published Jul 20, 2005• 1,139 citations
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Abstract

Decoy states have recently been proposed as a useful method for substantially improving the performance of quantum key distribution (QKD). Here, we present a general theory of the decoy state protocol based on only two decoy states and one signal state. We perform optimization on the choice of intensities of the two decoy states and the signal state. Our result shows that a decoy state protocol with only two types of decoy states---the vacuum and a weak decoy state---asymptotically approaches the theoretical limit of the most general type of decoy state protocol (with an infinite number of decoy states). We also present a one-decoy-state protocol. Moreover, we provide estimations on the effects of statistical fluctuations and suggest that, even for long-distance (larger than 100 km) QKD, our two-decoy-state protocol can be implemented with only a few hours of experimental data. In conclusion, decoy state quantum key distribution is highly practical.

DOI
10.1103/physreva.72.012326

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Decoy states have recently been proposed as a useful method for substantially improving the performance of quantum key distribution (QKD). Here, we present a general theory of the decoy state protocol based on only two decoy states and one signal state. We perform optimization on the choice of intensities of the two decoy states and the signal state. Our result shows that a decoy state protocol with only two types of decoy states---the vacuum and a weak decoy state---asymptotically approaches the theoretical limit of the most general type of decoy state protocol (with an infinite number of decoy states). We also present a one-decoy-state protocol. Moreover, we provide estimations on the effects of statistical fluctuations and suggest that, even for long-distance (larger than 100 km) QKD, our two-decoy-state protocol can be implemented with only a few hours of experimental data. In conclusion, decoy state quantum key distribution is highly practical.
Quantum key distribution (QKD) allows two parties to communicate in absolute security based on the fundamental laws of physics. Up till now, it is widely believed that unconditionally secure QKD based on standard Bennett-Brassard (BB84) protocol is limited in both key generation rate and distance because of imperfect devices. Here, we solve these two problems directly by presenting new protocols that are feasible with only current technology. Surprisingly, our new protocols can make fiber-based QKD unconditionally secure at distances over 100km (for some experiments, such as GYS) and increase the key generation rate from O(η2) in prior art to O(η) where η is the overall transmittance. Our method is to develop the decoy state idea (first proposed by W.-Y. Hwang in "Quantum Key Distribution with High Loss: Toward Global Secure Communication", Phys. Rev. Lett. 91, 057901 (2003)) and consider simple extensions of the BB84 protocol. This part of work is published in "Decoy State Quantum Key Distribution", . We present a general theory of the decoy state protocol and propose a decoy method based on only one signal state and two decoy states. We perform optimization on the choice of intensities of the signal state and the two decoy states. Our result shows that a decoy state protocol with only two types of decoy states—a vacuum and a weak decoy state—asymptotically approaches the theoretical limit of the most general type of decoy state protocols (with an infinite number of decoy states). We also present a one-decoy-state protocol as a special case of Vacuum+Weak decoy method. Moreover, we provide estimations on the effects of statistical fluctuations and suggest that, even for long distance (larger than 100km) QKD, our two-decoy-state protocol can be implemented with only a few hours of experimental data. In conclusion, decoy state quantum key distribution is highly practical. This part of work is published in "Practical Decoy State for Quantum Key Distribution", . We also have done the first experimental demonstration of decoy state quantum key distribution, over 15km of Telecom fibers. This part of work is published in "Experimental Decoy State Quantum Key Distribution Over 15km", .
The security of quantum-key-distribution system is analyzed using the decoy state protocol with two weak decoy states and one signal state. The comparison is based on the key generation rate as a function of distance for two types of decoy states: the vacuum and a weak decoy state, asymptotically approaching the theoretical limit of the most general type of decoy protocol, one-decoy-state protocol. We studied the two-decoy-state protocol in connection with the intensity of signal state, and the gain of signal states, the overall quantum bit error rate, the gain of single-photon states and the error rate of single-photon states and arrived at the optimal condition which maximizes the key generation rate.
Recently the performance of the quantum key distribution (QKD) is substantially improved by the decoy state method and the non-orthogonal encoding protocol, separately. In this paper, a practical non-orthogonal decoy state protocol with a heralded single photon source (HSPS) for QKD is presented. The protocol is based on 4 states with different intensities, i.e. one signal state and three decoy states. The signal state is for generating keys; the decoy states are for detecting the eavesdropping and estimating the fraction of single-photon and two-photon pulses. We have discussed three cases of this protocol, i.e. the general case, the optimal case and the special case. Moreover, the final key rate over transmission distance is simulated. For the low dark count of the HSPS and the utilization of the two-photon pulses, our protocol has a higher key rate and a longer transmission distance than any other decoy state protocol.
Decoy states have recently been proposed as a useful method for substantially improving the performance of quantum key distribution (QKD) protocols when a coherent-state source is used. Previously, data postprocessing schemes based on one-way classical communications were considered for use with decoy states. In this paper, we develop two data postprocessing schemes for the decoy-state method using two-way classical communications. Our numerical simulation (using parameters from a specific QKD experiment as an example) results show that our scheme is able to extend the maximal secure distance from 142km142\phantom{\rule{0.3em}{0ex}}\mathrm{km}142km (using only one-way classical communications with decoy states) to 181km181\phantom{\rule{0.3em}{0ex}}\mathrm{km}181km. The second scheme is able to achieve a 10% greater key generation rate in the whole regime of distances. We conclude that decoy-state QKD with two-way classical postprocessing is of practical interest.
It has been shown that in the asymptotic case of infinite-key length, the 2-decoy state Quantum Key Distribution (QKD) protocol outperforms the 1-decoy state protocol. Here, we present a finite-key analysis of the 1-decoy method. Interestingly, we find that for practical block sizes of up to 108 bits, the 1-decoy protocol achieves for almost all experimental settings higher secret key rates than the 2-decoy protocol. Since using only one decoy is also easier to implement, we conclude that it is the best choice for QKD, in most common practical scenarios.