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Physical Review A

Improving the performance of the four-state continuous-variable quantum key distribution by using optical amplifiers

Heng Zhang, Jian Fang, Guangqiang He

Published Aug 29, 2012• 75 citations
Publisher

Abstract

We propose a method to improve the secret key rates of four-state continuous-variable quantum key distribution by using an optical preamplifier. The modified protocol allows the distribution of higher secret key rates over long distances. Included in this paper is a detailed investigation of the effects of inserting an optical parametric amplifier into the output of the quantum channel in the four-state protocol, which will be instructive and meaningful about the usage of amplifiers in order to achieve the optimal performance of the protocol in a specific scenario.

DOI
10.1103/physreva.86.022338

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We propose a method to improve the secret key rates of four-state continuous-variable quantum key distribution by using an optical preamplifier. The modified protocol allows the distribution of higher secret key rates over long distances. Included in this paper is a detailed investigation of the effects of inserting an optical parametric amplifier into the output of the quantum channel in the four-state protocol, which will be instructive and meaningful about the usage of amplifiers in order to achieve the optimal performance of the protocol in a specific scenario.
Continuous-variable quantum key distribution protocols have been implemented recently, based on Gaussian modulation of the quadratures of coherent states. A present limitation of such systems is the finite efficiency of the detectors, that can in principle be compensated for by the use of classical optical preamplifiers. Here we study this possibility in detail, by deriving the modified secret key generation rates when an optical parametric amplifier is placed at the output of the quantum channel. After presenting a general set of security proofs, we show that the use of preamplifiers does compensate all the imperfections of the detectors when the amplifier is optimal in terms of gain and noise. Imperfect amplifiers can also enhance the system performance, under conditions which are generally satisfied in practice.
Continuous-variable quantum key distribution protocols, based on Gaussian modulation of the quadratures of coherent states, have been implemented in recent experiments. A present limitation of such systems is the finite efficiency of the detectors, which can in principle be compensated for by the use of classical optical preamplifiers. Here we study this possibility in detail, by deriving the modified secret key generation rates when an optical parametric amplifier is placed at the output of the quantum channel. After presenting a general set of security proofs, we show that the use of preamplifiers does compensate for all the imperfections of the detectors when the amplifier is optimal in terms of gain and noise. Imperfect amplifiers can also enhance the system performance, under conditions which are generally satisfied in practice.
Abstract Inherent defects of the detectors in a practical system cause deterioration of the performance of the unidimensional coherent-state continuous-variable quantum key distribution protocol. Aiming to achieve optimal performance, we propose a method of using a phase-sensitive amplifier to overcome the limitation that the detectors introduce. The modified protocol, corresponding to a higher key rate, provides the practical system with more robustness. To conduct a thorough investigation into the effects that the phase-sensitive amplifier creates, the expressions of the secret key rates are derived, under the conditions of coherent states, homodyne detection against collective attacks, and a phase-sensitive optical amplifier added at the output of the channel. Then, we carry out simulations to observe the performance in the cases of different gains. The simulation results demonstrate that the method we propose can improve the performance of the unidimensional protocol using coherent states and make up for the imperfections of the detector in a practical system.
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.