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Because of the unique advantages,continuous-variable quantum key distribution has been greatly developed in recent years.Because the devices used in the preparation and detection process of continuous-variable quantum key distribution are consistent with the classical optical communication,it has outstanding cost advantages and high reliability.In the past two decades,continuous-variable quantum key distribution with has achieved fruitful results.So far,some protocols have been proposed to simplify or improve the performance of quantum key distribution system,including unidimensional modulation protocols.Compared with Gaussian-modulated protocols,they have the advantages of simple modulation,low cost and only a few random numbers needed.However,like Gaussian-modulated protocols,the design of unidimensional modulation protocols is also based on device idealization.Some inherent characteristics in the actual device will make the actual performance of the protocol decline.The limited detection efficiency and extra electric noise of the actual homodyne detector will also make the secret key rate,secure transmission distance and other indicators of the protocol imperfect.In the Gaussian-modulated protocols,the current solution to this problem is usually to add optical amplifiers in the system.The optional solutions are to add phase-sensitive optical amplifiers in the system,noiseless linear amplifiers and so on.Among them,the phase-sensitive optical amplifier can amplify the selected direction signal without additional noise,which has unique advantages compared with other amplifiers.At present,the compensation effect of the phase-sensitive amplifier for the practical detector has been verified in the Gaussian-modulated protocols.In this thesis,based on the idea of compensation of the phase-sensitive amplifier to the practical homodyne detector of the Gaussian-modulated protocols,the phase-sensitive amplifier is applied to the unidimensional modulation protocols,and the calculation formula of the secret key rate after adding the phase-sensitive amplifier is derived,and the performance comparison before and after adding the phase-sensitive amplifier in the system is simulated.The research content mainly includes the theoretical security analysis of Gaussian-modulated protocols and unidimensional modulation protocols under collective eavesdropping,as well as the calculation method of secret key rate of Gaussian-modulated protocols and unidimensional modulation protocols after adding phase-sensitive optical amplifier.The results show that with the increase of amplification,the performance of the protocols is gradually improved,and finally it is infinitely close to the ideal performance of the detector.Therefore,the application of phase-sensitive optical amplifier improves the performance of the system,and it will play a huge potential in the future when building a long-distance and high-rate quantum key distribution network.