The Analysis Of The Security Of The Two-way Continuous-variable Quantum Key Distribution Protocol

Quantum key distribution (QKD) can enable two authentic parties, the sender (Alice)and the receiver (Bob), to obtain unconditional secret keys without restricting the powerof the eavesdropper (Eve). It has a widely application prospect due to its security is basedon the physical principle rather than the complexity of the mathematical calculation.Although the one-way continuous-variable QKD (CVQKD) has many merits, thesecret key rate is strongly afected by excess noise. To enhance the tolerable excess noise,the two-way CVQKD protocols are proposed. In this paper, we improve the original two-way CVQKD protocols and give its analysis of the security. The main researches of thispaper are described as follows.A family of new two-way CVQKD protocols are proposed and the security is ana-lyzed. Although the original two-way CVQKD protocols proposed by Stefano Pirandolacan remarkably enhance the tolerable excess noise, to analyze the security under gen-eral collective attack, it needs to construct the hybrid protocol where Alice randomlyswitches between one-way and two-way schemes for implementing the tomography ofthe quantum channels, which is complicated in practice. Therefore, we proposed a fea-sible modified two-way protocol by replacing the displacement operation of the originaltwo-way protocol with a passive operation on Alice’s side. Since Eve’s purification on the system of Alice and Bob can be obtained, the optimality of Gaussian attack can beused to analyze the security of the new two-way CVQKD protocols against collective en-tangling cloner attacks without the quantum-channel tomography. Thus the new protocolcan be applied more practically. The prepare-and-measure scheme of the new two-wayCVQKD protocol is also given. The simulation result indicates that the tolerable excessnoise in the new protocols surpasses that of the one-way CVQKD. Even if in the realexperimental values, the new two-way CVQKD protocols still outperform the one-wayprotocols in secret key rate and transmission distance.In addition, an improved two-way continuous-variable quantum key distribution pro-tocol with added noise is proposed and its security is analyzed. It has been proved thatadding a proper noise on Bob’s detection side in one-way CVQKD can enhance the se-cret key rate in reverse reconciliation. We apply the idea of adding noise to our modifiedtwo-way protocol to enhance the performance. Considering the correlation between thechannels, the security of the two-way CVQKD with added noise is analyzed and numeri-cal simulation against entangling cloner collective attacks is given. The simulation resultindicates that despite the secret key rate for the correlated channels is slightly lower thanthat for the uncorrelated channels when Eve inputs the equivalent variance of the modesinto the two channels, the performance of the two-way protocol is still far beyond that ofthe one-way protocols. In addition, the properly added noise is beneficial for enhancingthe secret key rate and the tolerable excess noise of the two-way CVQKD. The optimaltolerable excess noise of the two-way CVQKD with added noise is much more than thatof the one-way CVQKD. With the reasonable reconciliation efciency of90%, the two-way CVQKD with the added noise allows the distribution of secret keys over60km fiberdistance.