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Chinese Physics Letters

Four-State Modulation in Middle of a Quantum Channel for Continuous-Variable Quantum Key Distribution Protocol with Noiseless Linear Amplifier*

Yu Mao, Qi Liu, Ying Guo, Hang Zhang, Jian Zhou

Published Oct 1, 2019• 4 citations
Publisher

Abstract

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.

DOI
10.1088/0256-307x/36/10/100302

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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.
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.
In this paper, we first study a generalized protocol of discrete modulation for continuous-variable quantum key distribution with N coherent states in a Gaussian lossy and noisy channel and investigate its performance against collective attacks. We find that discrete modulation protocols with more than eight states do not perform better than the eight-state protocol. Then, we study the improvement of this protocol by using a nondeterministic noiseless linear amplifier (NLA) on Bob's detection stage. Results indicate that a NLA with gain g can extend the maximum transmission distance by 50 log10g2km and can increase the maximal tolerable excess noise. With the reconciliation efficiency β, we find the gain of NLA has a maximal value defined as gmaxand by adjusting the gain to about βgmaxone can have the best improvement on secret key rate.
In the continuous variable measurement-device-independent quantum key distribution (CV-MDI-QKD) protocol, both Alice and Bob send quantum states to an untrusted third party, Charlie, for detection through the quantum channel. In this paper, we mainly study the performance of the CV-MDI-QKD system using the noiseless linear amplifier (NLA). The NLA is added to the output of the detector at Charlie's side. The research results show that NLA can increase the communication distance and secret key rate of the CV-MDI-QKD protocol. Moreover, we find that the more powerful the improvement of the performance with the longer gain of NLA and the optimum gain is given under different conditions.
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.
We show that the maximum transmission distance of continuous-variable quantum key distribution in presence of a Gaussian noisy lossy channel can be arbitrarily increased using a heralded noiseless linear amplifier. We explicitly consider a protocol using amplitude- and phase-modulated coherent states with reverse reconciliation. Assuming that the secret key rate drops to zero for a line transmittance Tlim{T}_{\mathrm{lim}}Tlim​, we find that a noiseless amplifier with amplitude gain ggg can improve this value to Tlim/g2{T}_{\mathrm{lim}}/{g}^{2}Tlim​/g2, corresponding to an increase in distance proportional to logg\mathrm{log}glogg.