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arXiv:1205.0959 · Physical Review A

Improving the maximum transmission distance of continuous-variable quantum key distribution using a noiseless amplifier

Rémi Blandino, Anthony Leverrier, Marco Barbieri, Jean Etesse, Philippe Grangier, Rosa Tualle-Brouri

Published Jul 23, 2012• 139 citations
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Abstract

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 ${T}_{\mathrm{lim}}$, we find that a noiseless amplifier with amplitude gain $g$ can improve this value to ${T}_{\mathrm{lim}}/{g}^{2}$, corresponding to an increase in distance proportional to $\mathrm{log}g$.

DOI
10.1103/physreva.86.012327

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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.
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.
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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.