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Entropy

Improving the Maximum Transmission Distance of Self-Referenced Continuous-Variable Quantum Key Distribution Using a Noiseless Linear Amplifier

Yijun Wang, Xudong Wang, Duan Huang, Ying Guo

Published Jun 14, 2018• 2 citations
Publisher

Abstract

We show that a noiseless linear amplifier (NLA) can be placed properly at the receiver’s end to improve the performance of self-referenced (SR) continuous variable quantum key distribution (CV-QKD) when the reference pulses are weak. In SR CV-QKD, the imperfections of the amplitude modulator limit the maximal amplitude of the reference pulses, while the performance of SR CV-QKD is positively related to the amplitude of the reference pulses. An NLA can compensate the impacts of large phase noise introduced by the weak reference pulses. Simulation results derived from collective attacks show that this scheme can improve the performance of SR CV-QKD with weak reference pulses, in terms of extending maximum transmission distance. An NLA with a gain of g can increase the maximum transmission distance by the equivalent of 20log10g dB of losses.

DOI
10.3390/e20060461

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We show that a noiseless linear amplifier (NLA) can be placed properly at the receiver’s end to improve the performance of self-referenced (SR) continuous variable quantum key distribution (CV-QKD) when the reference pulses are weak. In SR CV-QKD, the imperfections of the amplitude modulator limit the maximal amplitude of the reference pulses, while the performance of SR CV-QKD is positively related to the amplitude of the reference pulses. An NLA can compensate the impacts of large phase noise introduced by the weak reference pulses. Simulation results derived from collective attacks show that this scheme can improve the performance of SR CV-QKD with weak reference pulses, in terms of extending maximum transmission distance. An NLA with a gain of g can increase the maximum transmission distance by the equivalent of 20log10g dB of losses.
The scheme of the self-referenced continuous-variable quantum key distribution (SR CV-QKD) has been experimentally demonstrated. However, because of the finite dynamics of Alice's amplitude modulator, there will be an extra excess noise that is proportional to the amplitude of the reference pulse, while the maximal transmission distance of this scheme is positively correlated with the amplitude of the reference pulse. Therefore, there is a trade-off between the maximal transmission distance and the amplitude of the reference pulse. In this paper, we propose the scheme of SR CV-QKD with virtual photon subtraction, which not only has no need for the use of a high intensity reference pulse to improve the maximal transmission distance, but also has no demand of adding complex physical operations to the original self-referenced scheme. Compared to the original scheme, our simulation results show that a considerable extension of the maximal transmission distance can be obtained when using a weak reference pulse, especially for one-photon subtraction. We also find that our scheme is sensible with the detector's electronic noise at reception. A longer maximal transmission distance can be achieved for lower electronic noise. Moreover, our scheme has a better toleration of excess noise compared to the original self-referenced scheme, which implies the advantage of using virtual photon subtraction to increase the maximal tolerable excess noise for distant users. These results suggest that our scheme can make the SR CV-QKD from the laboratory possible for practical metropolitan area application.
Developing quantum key distribution (QKD) protocols resistant to losses and noises is of great importance in practice. We show that the maximum transmission distance and tolerable excess noise of the Gaussian modulation (GM) and discrete modulation (DM) CVQKD protocols can be dramatically increased by using a noiseless linear amplifier (NLA). It is proved that a NLA with gain g can increase the maximum transmission distance by 20 /αlog10g km, where a = 0.2 dB/km is the loss coefficient of the fiber channel.
A modified four-state CVQKD protocol is proposed to increase the maximum transmission distance and tolerable excess noise in the presence of Gaussian lossy and noisy channel by using a noiseless linear amplifier (NLA). An ideal NLA with gain ggg can increase the maximum admission losses by 20log10g20{\mathrm{log}}_{10}g20log10​g dB. Further, the imperfections in a practical NLA, such as the finite detection efficiency and imperfect single-photon source, are included in consideration.
We characterize a modified continuous-variable quantum key distribution (CV-QKD) protocol with four states in the middle of a quantum channel. In this protocol, two noiseless linear amplifiers (NLAs) are inserted before each detector of the two parts, Alice and Bob, with the purpose of increasing the secret key rate and the maximum transmission distance. We present the performance analysis of the new four-state CV-QKD protocol over a Gaussian lossy and noisy channel. The simulation results show that the NLAs with a reasonable gain g can effectively enhance the secret key rate as well as the maximum transmission distance, which is generally satisfied in practice.
We show that the successful use of a noiseless linear amplifier (NLA) can help increase the maximum transmission distance and tolerate more excess noise of the plug-and-play dual-phase-modulated continuous-variable quantum key distribution. In particular, an equivalent entanglement-based scheme model is proposed to analyze the security, and the secure bound is derived with the presence of a Gaussian noisy and lossy channel. The analysis shows that the performance of the NLA-based protocol can be further improved by adjusting the effective parameters.