# Performance Analysis of Continuous-Variable Quantum Key Distribution with Multi-Core Fiber
## 3 Performance Analysis  
We have demonstrated the characteristics of the MCF-based CVQKD system. Figure 4 depicts the MCF-based CVQKD protocol, including the one-way or two-way CVQKD protocols [8; 17] and the MDI CVQKD protocol [38]. The global parameters that are used for simulations are the fiber loss coefficient \(\alpha\) and the electronic noise \(v_{el}\), quantum efficiency \(\eta\) of the homodyne detector and the system excess noise \(\epsilon_{0}\), the reconciliation efficiency \(\beta\) and the insert loss of the FIFO \(\eta_{F}\). All the above parameters are given in simulations with the values \(\alpha=0.2\) dB/km, \(v_{el}=0.01N_{0}\), \(\eta=0.719\), \(\epsilon_{0}=0.01N_{0}\), \(\beta=0.95\) and \(\eta_{F}=1.1\) dB, 0.5 dB or 0 dB, respectively [8; 14; 28]. For the one-way CVQKD protocol, the secure key rate with reverse reconciliation under collective attacks is given by [8; 17]  
\[K=\beta I_{AB}-\chi_{BE}, \tag{6}\]  
where \(I_{AB}\) is the Shannon mutual information between [PERSON] and [PERSON], and \(\chi_{BE}\) is the Holevo bound in the information between [PERSON] and [PERSON]. A gives the calculations of \(I_{AB}\) and \(\chi_{BE}\). The numerical results of the one-way protocol are shown in Figure 5, where (a) and (b) represent the results of the transmitted LO scheme while (c) and (d) represent the results of the locally generated LO schemes. Here [PERSON]'s modulation \(V_{A}\) is set to \(4N_{0}\) and \(20N_{0}\) in Figure 5a,b, and \(40N_{0}\) in Figure 5c,d, respectively. As shown in Figure 5 we find that although the secret key rate of one-core-based CVQKD may be slightly smaller than that of the original SMF-based CVQKD, the total secret key rate is still improved for the MCF-based system. The decreasing secret key rate of one-core-based CVQKD is due to the insert loss of the FIFO. When this insert loss decreases to a threshold, its impact can be nearly neglected, as the violet lines shown in Figure 5a,b, where the insert loss of the FIFO is set to 0.5 dB. We can also find that the insert loss of the FIFO has less influence to the transmitted LO scheme than the locally generated LO scheme, especially when \(V_{A}\) is close to the optimal value of \(4N_{0}\). This result can also be reflected by the simulation of tolerable excess noise. We have shown the tolerable excess noise for one-way protocols in Figure 5e,f, when \(\eta_{F}\) takes different values. It shows that the locally generated LO scheme is more sensitive to the insert loss of the FIFO. Therefore, with lower insert loss of the FIFO and more cores of MCF, the performance of the MCF-based one-way CVQKD protocols can be improved better. We note that the numerical results of the two-way protocol is similar to that of the one-way protocol, and hence can be ignored for simplicity. Figure 4: The MCF-based CVQKD protocols. (**a**) The one-way or two-way CVQKD protocol. (**b**) The MDI CVQKD protocol. FIFO: fan-in/fan-out. Figure 5: The secret key rate and the tolerable excess noise of MCF-based one-way CVQKD protocols, when using different values of \(\eta_{F}\). (**a**) CVQKD with transmitted LO for \(V_{A}=4N_{0}\). (**b**) CVQKD with transmitted LO for \(V_{A}=20N_{0}\). (**c**) CVQKD with locally generated LO for \(V_{R}=100V_{A}\). (**d**) CVQKD with locally generated LO for \(V_{R}=50V_{A}\). (**e**) The tolerable excess noise for the transmitted LO scheme. (**f**) The tolerable excess noise for the locally generated LO scheme. In the results of secret key rate, the black lines are for the SMF-based system, the red dotted lines are for the one-core-based system, the blue lines are for the 7-core-based system and the green dash dotted lines are for the 30-core-based system, the violet solid lines are the results for the case of using SMF, i.e., \(\eta_{F}=0\) dB.