## 2 Theoretical Framework and Simulation Experiment Setup  
Figure 1 displays the fundamental block diagram of a quad-channel COCSC system, built on four concurrent photonic reservoir computers. This intricate system is composed of the transmitter module (TM), the reservoir computing module (RCM), and the coherent demodulation module (CDM). Within the TM, the ground state of the QD-spin-VSEL generates the chaotic X-PC and Y-PC, marked as GS-PC\({}_{x}\) and GS-PC\({}_{y}\), respectively. Interestingly, its excited state yields two additional photonic currents recognizable as ES-PC\({}_{x}\) and ES-PC\({}_{y}\). Each of the QPSK, 4 QAM, 8 QAM and 16 QAM is IQ modulated with a group of bit sequences (baseband signal). In this scheme, there are four distinct groups of bit sequence signals, as depicted as \(b^{1}\)-\(b^{4}\), individually. For the convenience of discussion, the temporal dynamics of the QPSK, 4 QAM, 8 QAM and 16 QAM are described by \(S_{1}(t)\), \(S_{2}(t)\), \(S_{3}(t)\) and \(S_{4}(t)\), respectively. The QPSK, 4 QAM, 8 QAM and 16 QAM are masked within the chaotic GS-PC\({}_{x}\), GS-PC\({}_{y}\), ES-PC\({}_{x}\) and ES-PC\({}_{y}\), respectively. These four channels of chaotic masked signals are integrated into a single optical fiber utilizing a wavelength division multiplexer (WDM Mux). In the RCM, after fiber transmission, the combined signals are partitioned into four-channel chaotic masked signals via a wavelength division demultiplexer (WDM DeMux). Each channel of chaotic masked signal is subsequently bisected into dual beams. A singular beam of chaotic masked signal is introduced to a photonic RC. Here, the predicted outputs from the RC\({}_{1}\)-RC\({}_{4}\) are denoted as the GS-PC\({}_{x}^{{}^{\prime}}\), GS-PC\({}_{y}^{{}^{\prime}}\), ES-PC\({}_{x}^{{}^{\prime}}\) and ES-PC\({}_{y}^{{}^{\prime}}\), respectively. Once output weights are precisely trained within the non-linear node states of each photonic RC, the GS-PC\({}_{x}\), GS-PC\({}_{y}\), ES-PC\({}_{x}\) and ES-PC\({}_{y}\) can be perfectly synchronized with GS-PC\({}_{x}^{{}^{\prime}}\), GS-PC\({}_{y}^{{}^{\prime}}\), ES-PC\({}_{x}^{{}^{\prime}}\) and ES-PC\({}_{y}^{{}^{\prime}}\) correspondingly. In this scenario, signal types QPSK, 4 QAM, 8 QAM and 16 QAM can be demodulated by applying synchronous subtraction between the chaotic masked signal and each RC's predicted output. These demodulated messages, noted as \(S_{1}^{{}^{\prime}}(t)\), \(S_{2}^{{}^{\prime}}(t)\), \(S_{3}^{{}^{\prime}}(t)\) and \(S_{4}^{{}^{\prime}}(t)\), are then channeled into their respective coherent demodulation units (CDUs with the subscripts of 1-4). Post coherent demodulation and DSP, four sets of bit sequence signals are further decoded. These reinstated signal bits are referred to as \(b^{1}\)-\(b^{4}\), respectively. Following the principal block diagram displayed in Figure 1, Figure 2a,b illustrate the simulation experiment setup for a four-channel COCSC system. In this configuration, the QD spin-VCSEL marked with subscript 1 functions as the driving laser, while the QD spin-VCSEL designated by subscript 2 serves as the reserve laser. The CWs, labelled from 1-8, represent the continuous wave lasers. Optical Isolators (ISs, with subscripts from 1-12) are put into service to prevent optical feedback. The neutral density filters (NDFs, labelled from 1-10) are employed to regulate light intensity. The QPSK transmitter (QPSKT), 4 QAM  
Figure 1: Principle block diagram of four-channel coherent optical chaotic secure communication based on four parallel photonic reservoir computers.