# Performance Analysis of Continuous-Variable Quantum Key Distribution with Multi-Core Fiber
## 2 The MCF-Based CVQKD
We do not show the impact of the quantum signal pulse as its impact is much lower than the weak reference pulse's, although the quantum signal pulse's impact will be non-negligible when \(h_{mn}\geq-80\) dB/km, \(\langle N_{sig}^{out}\rangle=10\) and \(\Delta_{t}^{s}=0\). We also do not show the contribution of the LO, as its mean photon number (\(10^{8}\) as usual) is much larger than the weak reference pulse so that its excess noise contribution is unbearable. Consequently, the excess noise contributed by the inter-core crosstalk may become very large for the MCF-based CVQKD when the wavelengths of quantum channels in all cores are equal, even though the using of the ultra-low crosstalk MCF. In practice, for the improvement of the communication capacity, we should use a smaller core pitch and hence more cores MCF, leading to a larger coupling coefficient. Therefore, an effective suppression of the impact of the inter-core crosstalk can increase the secure key rate of MCF-based CVQKD system. Note, the calculations above assume that the time delay of \(\Delta_{t}^{r}\) and \(\Delta_{t}^{s}\) between pulses are invariable. This assumption may not follow the real situation when we use heterogeneous MCF, but this does not affect our analysis above as we can use an average value to take the estimation. Figure 2: The excess noise contributed from the weak reference pulse as a function of the transmission distance and \(\Delta_{t}^{r}\). SUN, shot noise units. To suppress the impact of the inter-core crosstalk to the quantum channel, we consider this problem in three points. First, we can monitor pulses time delay between cores constantly. This method is feasible for few-core and low-speed MCF-based CVQKD system as the pulse period is large and the adjacent cores of one core is few. However, this approach will increase the system's cost, which is increased with the system's core number and the repetition rate. Therefore, it is not a good solution. Second, we consider using a low coupling coefficient MCF so that the excess noise contributed by the inter-core crosstalk is lower than \(0.001N_{0}\) (\(N_{0}\) is the shot noise), and hence this excess noise can be neglected [35]. This method is straightforward. However, it will bring about challenges of MCF fabrication technique or decrease the total communication capacity of the system. Take the central core of a 7-core MCF for example. For the transmitted LO scheme, the coupling coefficient should be lower than \(-157\) dB/km when the output mean photon number of the LO is \(10^{8}\). It is so hard to fabricate a so low coupling coefficient MCF, when maintaining a relatively small core pitch (\(45\)\(\upmu\)m for example [31]). For the locally generated LO scheme, the conservative value of the coupling coefficient should be lower than \(-107\) dB/km when the mean photon number of the weak phase reference pulse is \(1000\). The fabrication of this value of coupling coefficient for MCF is also a challenge. Actually, one can increase the core pitch to decrease the coupling coefficient of MCF, but this approach will also decrease the core density of MCF and degrade the total communication capacity indirectly. Therefore, using a low coupling coefficient MCF to remove the impact of inter-core crosstalk is not preferred in practice. Note, the excess noise should be the sum of all the adjacent cores' contributions, and the conservative estimation of the coupling coefficient above is under the assumption of \(\Delta_{t}^{r}=0\) and \(L=100\) km. Third, we consider staggering the wavelength of quantum channel in each core. If the wavelength of the inter-core crosstalk differs from the wavelength of the quantum channel, it can be removed by filtering technology at the receiver [36]. Moreover, the mode selection of the LO can restrict this noise further [37]. Consequently, this method can be ready to realize in present technology and appears good at noise suppressing.