## 3 Results and Discussions  
The parameter values for the driving quantum dot (QD) spin-vertical cavity surface-emitting laser (VCSEL) are detailed in Table 1, while those for the reservoir QD spin-VCSEL are outlined in Table 2. Our initial step is to model the power spectral density (PSD) profiles and temporal samples stemming from the driving QD spin-VCSEL, employing concurrent simulations within Matlab (version R2021a) and VPI (version 11.1) software environments. Within Matlab, Equations (1)-(5) are executed via the fourth-order Runge-Kutta numerical approach, adopting a time step (\(h\)) of 0.78 ps. The sampling periods for the four distinct input data streams (\(u_{Gx}(n-L_{Gx})\), \(u_{Gy}(n-L_{Gy})\), \(u_{Ex}(n-L_{Ex})\), \(u_{Ey}(n-L_{Ey})\)) are denoted by \(T\) and are uniformly set at 10 ps. The constants \(L_{Gx}\), \(L_{Gy}\), \(L_{Ex}\) and \(L_{Ey}\) are all given the value of 2.0513 \(\times\) 10\({}^{4}\), which is based on \(\tau_{x}\), \(\tau_{y}\) being 16 ns and \(h\) amounting to 0.78 ps. Concurrently, the dynamical output from the four parallel reservoirs, utilizing the reservoir QD spin-VCSEL, is also modeled with the integration of Matlab and VPI, where Equations (6)-(10) are solved through the fourth-order Runge-Kutta method with a finer time step of 0.048 ps. Within the present framework, both the encoding rate of the messages and the data processing speed of the reservoirs are influenced by the effective bandwidths of the driving and reservoir VCSELs. Figure 3a-d depict the PSD distributions of the GS-PC\({}_{x}\) and GS-PC\({}_{y}\), as well as the ES-PC\({}_{x}\) and ES-PC\({}_{y}\) emitted by the driving QD spin-VCSEL. According to the representations in Figure 3, the PSD distributions for these PCs consistently demonstrate chaotic behavior. The effective 3 dB bandwidths for both the GS-PC\({}_{x}\) and GS-PC\({}_{y}\) are calculated to be 180 GHz, whereas the ES-PC\({}_{x}\) and ES-PC\({}_{y}\) are slightly higher at 200 GHz. Correspondingly, the effective 3 dB bandwidths for the GS-PC\({}_{x}^{\prime}\), GS-PC\({}_{y}^{\prime}\), ES-PC\({}_{x}^{\prime}\) and ES-PC\({}_{y}^{\prime}\) of the reservoir system exhibit similar characteristics to those of their driving system counterparts (GS-PC\({}_{x}\), GS-PC\({}_{y}\), ES-PC\({}_{x}\) and ES-PC\({}_{y}\), respectively). These outcomes suggest that our system is capable of achieving high-speed, four-channel coherent optical chaotic secure communications. \begin{table}
\begin{tabular}{c c c c} \hline
**The Parameter and Symbol** & **Value** & **The Parameter and Symbol** & **Value** \\ \hline The photon decay rate \(\kappa_{D}\) & 250 ns\({}^{-1}\) & The capture rate \(\gamma_{D,0}\) & 400 ns\({}^{-1}\) \\ Linewidth enhancement factor \(\alpha_{D}\) & 3 & Intradot relaxation rate \(\gamma_{D,21}\) & 50 ns\({}^{-1}\) \\ Total pump intensity \(\eta\) & 4 & Spin relaxation rate \(\gamma_{D,s}\) & 10 ns\({}^{-1}\) \\ Dichroism \(\gamma_{D,a}\) & 0 ns\({}^{-1}\) & Carrier recombination rate \(\gamma_{D,n}\) & 1 ns\({}^{-1}\) \\ Birefringence \(\gamma_{D,p}\) & 30 ns\({}^{-1}\) & Electron charge \(e\) & 1.6 \(\times\) 10\({}^{-19}\) C \\ Quantum dot density \(N_{QD}\) & 1.5 \(\times\) 10\({}^{17}\) m\({}^{-2}\) & The gain coefficient \(h_{D,1}\) & 1.1995 \\ \hline \end{tabular}
\end{table} 
Table 1: Parameter values of the driving QD Spin-VCSEL. The chaotic GS-PC\({}_{x}^{\prime}\), GS-PC\({}_{y}^{\prime}\), ES-PC\({}_{x}^{\prime}\) and ES-PC\({}_{y}^{\prime}\) produced by the reservoir QD spin-VCSEL, as four parallel reservoirs, are utilized to perform the predictions of the delayed outputs GS-PC\({}_{x}\), GS-PC\({}_{y}\), ES-PC\({}_{x}\) and ES-PC\({}_{y}\), respectively. We collect 5096 samples of these delayed outputs at a sampling interval of 10 ps. After discarding the initial 1000 samples to remove transients, we allocate 2048 samples for training each of the four reservoirs, and an equivalent number of subsequent points for testing the corresponding reservoir.