## 2 Theoretical Framework and Simulation Experiment Setup
Here, TM: transmitter module; RCM: reservoir computing module; CDM: coherent demodulation module; CDU: coherent demodulation unit; \(b^{1}\)–\(b^{4}\): baseband signals (bit sequence signals); \(b^{1}\)–\(b^{4}\): demodulation baseband signals; GS-PC\({}_{x}\) and GS-PC\({}_{y}\): X-PC and Y-PC from the ground state emission of the QD-spin-VCSEL, respectively; WDM Mux: wavelength division multiplexer; WDM DeMux: wavelength division demultiplexer; and ES-PC\({}_{x}\) and ES-PC\({}_{y}\): X-PC and Y-PC from the excited state emission of the QD-spin-VCSEL, respectively. transmitter (4 QAMT), 8 QAM transmitter (8 QAMT) and 16 QAM transmitter (16 QAMT) generate QPSK, 4 QAM, 8 QAM and 16 QAM signals, respectively. The fiber polarization beam splitters (FPBS), carrying subscripts 1-6, are used to partition the light into two distinct polarization components. Bidirectional ports (BPs, labelled 1-4) combine two bidirectional ports into a singular bidirectional multiport of width 2. Lastly, photodiodes (PDs), labeled from 1-12, are designated to convert light waves into corresponding current signals. Figure 2: Simulation experiment setup of a four-channel COSC system, founded on four parallel reservoirs. Here, (**a**) Transmitter; (**b**) Chaos-synchronization prediction and demodulation using reservoirs; (**c**) Coherent demodulation and DSP processing; PL: pumped light; PCL: polarization controller; IS: isolator; FPBS: fiber-optic polarization splitter; QPSK: QPSK transmitter; 4 QAMT: 4 QAM transmitter; 8 QAMT: 8 QAM transmitter; 16 QAMT: 16 QAM transmitter; NS: empty source; BP: bidirectional ports; PC: power combiner; FPC: fiber polarization coupler; WDM Mux: wavelength division multiplexer; WDM DeMux: wavelength division demultiplexer; CW: continuous wave laser; NDF: the neutral density filter; PD: photodetector; AM: amplitude modulator; DL: delay line; FC: fiber coupler; OL: output layer; CSM: co-simulation module; EA: Electrical amplifier; DM: discrete module; SC: proportional operation circuit; Mask: masked signal; PDDCR: polarization-diversity digital coherent receiver; DSP: digital signal processor; SF: submatrix finder; BEREM: bit error rate estimation module; and NA: numerical analyzer. In Figure 2a,b, in the QPSKT, the QPSK modulation scheme utilizes a baseband signal \(b^{1}\) for its in-phase (I) and quadrature (Q) components. Similarly, in the 4 QAMMT, for 4 QAM modulation, the I and Q components are modulated using the odd and even parts of the signal \(b^{2}\). In the 8 QAMMT, for 8 QAM modulation, the odd and even parts of the signal \(b^{3}\) are used as the respective signals for the I and Q components. Lastly, for 16 QAM modulation, the I and Q components are modulated using the odd and even parts of the signal \(b^{4}\). In these four modules (QPSKT, 4 QAMMT, 8 QAMMT and 16 QAMT), QPSK, 4 QAM, 8 QAM and 16 QAM signals are optically modulated using continuous wave lasers and then converted into optical signals at the output ports of these modules. In the QD spin-VCSEL labeled with subscript 1, the light emitted from its ground state (GS) is divided into two chaotic polarization components (GS-PC\({}_{x}\) and GS-PC\({}_{y}\)) using the FPBS\({}_{1}\), with their amplitudes represented as \(E_{Gx}(t)\) and \(E_{Gy}(t)\), respectively. Likewise, the light emitted from its excited state (ES) is separated into two chaotic polarization components (ES-PC\({}_{x}\) and ES-PC\({}_{y}\)) using the FPBS\({}_{2}\), and their amplitudes are indicated by \(E_{Ex}(t)\) and \(E_{Ey}(t)\), respectively. The QPSK and 4 QAM signals are concealed within the chaotic GS-PC\({}_{x}\) and GS-PC\({}_{y}\) using the power combiners 1 and 2 (PC\({}_{1}\) and PC\({}_{2}\)), respectively. These two chaotic hidden signals can be described as (\(E_{Gx}(t)+S_{1}(t)\)) and (\(E_{Gy}(t)+S_{2}(t)\)), respectively, and are combined into a single beam through the fiber polarization coupler 1 (FPC\({}_{1}\)).