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arXiv:quant-ph/0609137 · Applied Physics Letters

Simple protocol for secure decoy-state quantum key distribution with a loosely controlled source

Xiang‐Bin Wang, Cheng-Zhi Peng, Jian-Wei Pan

Published Jan 15, 2007• 48 citations
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Abstract

The method of decoy-state quantum key distribution requests different intensities of light pulses. Existing theory has assumed exact control of intensities. Here the authors propose a simple protocol which is secure and efficient even there are errors in intensity control. In their protocol, decoy pulses and signal pulses are generated from the same father pulses with a two-value attenuation. Given the upper bound of fluctuation of the father pulses, their protocol is secure provided that the two-value attenuation is done exactly. They propose to use unbalanced beam splitters for a stable attenuation.

DOI
10.1063/1.2431718

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The method of decoy-state quantum key distribution requests different intensities of light pulses. Existing theory has assumed exact control of intensities. Here the authors propose a simple protocol which is secure and efficient even there are errors in intensity control. In their protocol, decoy pulses and signal pulses are generated from the same father pulses with a two-value attenuation. Given the upper bound of fluctuation of the father pulses, their protocol is secure provided that the two-value attenuation is done exactly. They propose to use unbalanced beam splitters for a stable attenuation.
In this paper, we present a scheme on realizing the passive decoy-state quantum key distribution. In this scheme, two weak coherent pulses interfere at a beam-splitter, and pulses in one output port are split by one beam-splitter into two parts which are sent into two local detectors individually. Then, all the clicking and nonclicking events from the local detectors are used to herald the arriving and nonarriving of the signal pulse in the other output port. Accordingly, we can obtain more decoy states in the photon-number space and can thus, achieve more precise estimations for single-photon contributions. In this scheme, we use only one intensity at each input of the beam-splitter to avoid intensity modulation fluctuations existing in other active decoy-state methods. We compare the present scheme with Curty et al.'s passive scheme and the conventional three-intensity decoy-state scheme with the weak coherent sources. Through numerical simulations, we demonstrate that this scheme is better than the other two methods.
The security of decoy-state quantum key distribution (QKD) highly depends on the accurate control of multiple intensity states. Although several theoretical studies on the QKD with loosely controlled source intensities have been proposed, there is still a large gap between the experimental realization and the theoretical analysis. In this paper, we adopt the gain-switching method to generate short optical pulses, and the corresponding intensity stabilities are quantitatively measured. The method via optical injection is proposed to make effective reductions of the intensity fluctuations from 6.47%∼1.59% to 1.95%∼1.15% at different optical powers. QKD performance adopting the experimental results is also analyzed and discussed. For a typical 40 dB high-attenuation QKD system, the relative increase on the secure key rates reaches 51.89% for the corresponding intensity fluctuations of 1.15% with optical injection and 1.59% without optical injection. The presented intensity-stable optical pulse source can find wide applications in different QKD protocols, such as BB84, DPS, COW, etc.
Secure quantum key distribution can be achieved with an imperfect single-photon source through implementing the decoy-state method. However, security of all those theoretical results of decoy-state method based on the original framework raised by Hwang needs monitoring the source state very carefully, because the elementary proposition that the counting rates of the same state from different sources are equal does not hold in general when the source is unstable. Source intensity monitoring greatly decreases the system efficiency. Here without using Hwang's proposition for stable source, we present a sufficient condition for a secure decoy-state protocol without monitoring the source intensity. The passive 2-intensity protocol proposed by Adachi, Yamamoto, Koashi, and Imoto(AYKI) (Phys. Rev. Lett. 99, 180503 (2007) satisfies the condition. Therefore, the protocol can always work securely without monitoring the source state or switching the source intensity. We also show that our result can greatly improve the key rate of the 3-intensity protocol with a fluctuating coherent-state source.
We show how to do decoy-state quantum key distribution efficiently with large random errors in the intensity control. We present a theorem for efficiently calculating the lower bound of single-photon counts with many undetermined parameters. In the calculation of the single-photon counts of our protocol, the linear terms of the intensity fluctuation disappear and only the quadratic terms take effect. Given that the intensity fluctuation is upper bounded by $\ifmmode\pm\else\textpm\fi{}5%$, $\ifmmode\pm\else\textpm\fi{}10%$, and $\ifmmode\pm\else\textpm\fi{}15%$, the verified lower bound of the percentage of untagged bits from our protocol is as large as 99.7%, 99.0%, and 97.9% of that from an ideal protocol where the light intensity is exactly controlled.
The decoy-state protocol has been considered to be one of the most important methods to protect the security of quantum key distribution (QKD) with a weak coherent source. Here we test two experimental approaches to generating the decoy states with different intensities: modulation of the pump current of a semiconductor laser diode, and external modulation by an optical intensity modulator. The former approach shows a side channel in the time domain that allows an attacker to distinguish s signal state from a decoy state, breaking a basic assumption in the protocol. We model a photon-number-splitting attack based on our experimental data, and show that it compromises the system's security. Then, based on the work of Tamaki et al. [New J. Phys. 18, 065008 (2016)], we obtain two analytical formulas to estimate the yield and error rate of single-photon pulses when the signal and decoy states are distinguishable. The distinguishability reduces the secure key rate below that of a perfect decoy-state protocol. To mitigate this reduction, we propose to calibrate the transmittance of the receiver (Bob's) unit. We apply our method to three QKD systems and estimate their secure key rates.