## 2 Theoretical Framework and Simulation Experiment Setup
The 8 QAM and 16 QAM signals are masked within the ES-PC\({}_{x}\) and ES-PC\({}_{y}\) using the PC\({}_{3}\) and PC\({}_{4}\), respectively. These two chaotic masked signals are represented as (\(E_{Ex}(t)+S_{3}(t)\)) and (\(E_{Ey}(t)+S_{4}(t)\)), respectively, and merged into a single beam via FPC\({}_{2}\). The mixed light-waves from FPC\({}_{1}\) and FPC\({}_{2}\) are coupled into an optical fiber through the WDM Mux. After fiber transmission, the multiplexed light-waves are split into two beams with different wavelengths via the WDM DeMux. One beam of light from the WDM DeMux is divided into GS-PC\({}_{x}\) and GS-PC\({}_{y}\), which contain hidden messages, via the FPBS\({}_{3}\). The GS-PC\({}_{x}\), carrying the QPSK signal, is further split into two parts using the fiber beam splitter 1 (FBS\({}_{1}\)). One part is injected into input layer 1, and the other is converted into a current signal by the PD\({}_{5}\). The GS-PC\({}_{y}\) with 4 QAM, ES-PC\({}_{x}\) with 8 QAM and ES-PC\({}_{y}\) with 16 QAM are processed similarly. The input layers provide the connections to the reservoirs. Initially, in input layers 1 and 2, the GS-PC\({}_{x}\), including QPSK and the GS-PC\({}_{y}\) with 4 QAM, are transformed into two distinct current signals via the PD\({}_{1}\) and PD\({}_{2}\), amplified using electric amplifiers EA\({}_{1}\) and EA\({}_{2}\), and eventually sampled as separate input data series through the discrete modules DM\({}_{1}\) and DM\({}_{2}\), respectively. These data series are designated as \(u_{Gx}(n\!-\!L_{Gx})\) and \(u_{Gy}(n\!-\!L_{Gy})\). Moreover, the sampled time series of the QPSK, 4 QAM, 8 QAM and 16 QAM are respectively described as \(I_{1}(n)\), \(I_{2}(n)\), \(I_{3}(n)\) and \(I_{4}(n)\), where \(I_{1}(n)=|S_{1}(n)|^{2}\), \(I_{2}(n)=|S_{2}(n)|^{2}\), \(I_{3}(n)|=|S_{3}(n)|^{2}\) and \(I_{4}(n)=|S_{4}(n)|^{2}\). As a result, \(u_{Gx}(n\!-\!L_{Gx})=(C_{Gx}(n\!-\!L_{Gx})+I_{1}(n\!-\!L_{Gx}))\), \(u_{Gy}(n\!-\!L_{Gy})=(C_{Gy}(n\!-\!L_{Gy})+I_{2}(n\!-\!L_{Gy}))\), where \(C_{Gx}(n\!-\!L_{Gx})=|E_{Gx}(n-\!L_{Gx})|^{2}\) and \(C_{Gy}(n\!-\!L_{Gy})=|E_{Gy}(n-\!L_{Gy})|^{2}\). The term \(n\) denotes the discrete time index, while \(L_{Gx}\) and \(L_{Gy}\) signify the discrete channel delay lengths for GS-PC\({}_{x}\) and GS-PC\({}_{y}\), respectively. Input layers 3 and 4 process ES-PC\({}_{x}\) containing 8 QAM and ES-PC\({}_{y}\) carrying 16 QAM in a similar manner, yielding respective input data as \(u_{Ex}(n\!-\!L_{Ex})\) and \(u_{Ey}(n\!-\!L_{Eg})\). Here, \(u_{Ex}(n\!-\!L_{Ex})\) equals (\(C_{Ex}(n\!-\!L_{Ex})+I_{3}(n\!-\!L_{Ex})\)) and \(u_{Ey}(n\!-\!L_{Eg})\) corresponds to (\(C_{Ey}(n\!-\!L_{Eg})+I_{4}(n\!-\!L_{Eg})\)), where \(C_{Ex}(n\!-\!L_{Ex})=|E_{Ex}(n-\!L_{Ex})|^{2}\) and \(C_{Ey}(n\!-\!L_{Eg})\)\(=|E_{Ey}(n-\!L_{Eg})|^{2}\). \(L_{Ex}\) represents the discrete channel delay length for the ES-PC\({}_{x}\) and \(L_{Eg}\) illustrates that of the ES-PC\({}_{y}\). Importantly, \(C_{Gx}(n\!-\!L_{Gx})\), \(C_{Gy}(n\!-\!L_{Gy})\), \(C_{Ex}(n\!-\!L_{Ex})\) and \(C_{Ey}(n\!-\!L_{Eg})\) are considered four distinct prediction targets. The sampled data, \(u_{Gx}(n\!-\!L_{Gx})\) and \(u_{Ex}(n\!-\!L_{Ex})\), are multiplied by the mask signal, Mask\({}_{x}\), while \(u_{Gy}(n\!-\!L_{Gy})\) and \(u_{Ey}(n\!-\!L_{Eg})\) are multiplied by Mask\({}_{y}\). Both Mask\({}_{x}\) and Mask\({}_{y}\) are chaotic signals, as illustrated in [24]. Post scaling with a scaling factor \(\gamma\) through the scaling operation circuits (SC\({}_{1}\)-SC\({}_{4}\)), the four input layers yield output signals denoted as \(S_{Gx}(n)\), \(S_{Gy}(n)\), \(S_{Ex}(n)\) and \(S_{Ey}(n)\), respectively. These are respectively modulated with the optical-field phases of CW\({}_{1}\)-CW\({}_{4}\). The FPC\({}_{3}\) first couples the modulated \(S_{Gx}(n)\) and \(S_{Gy}(n)\) into a single beam, which is then injected into the ground state of the reservoir QD spin-VCSEL.