## 1 Introduction
Furthermore, these lasers can achieve ultrafast operation from both their ground and excited states, presenting promising opportunities for ultrafast dual-wavelength laser modules that emit ultrafast dynamics. Each beam of light emitted from the ground state (GS) and excited state (ES) includes components with right circular polarization (RCP) and left circular polarization (LCP). The utilization of ultrafast chaotic RCPs and LCPs from the ground and excited states holds significant potential for realizing a four-channel COCSC system with high speed and high capacity. However, one of the challenges in such a COCSC system pertains to achieving high-quality chaotic synchronization and coherent demodulation. Traditional chaotic synchronization methods, such as leading synchronization and lagging synchronization, are limited by the symmetry between the driving laser and the response laser, as well as the need for a perfect match of their parameters. However, recently developed photon reservoir computing (RC) systems have demonstrated promising performances in chaotic synchronization prediction and chaotic signal separation. These RC systems are expected to alleviate the challenges faced in high-speed COCSC. In particular, a QD spin-VCSEL can generate four polarization components (PCs) from the GS and ES emissions. Four parallel RCs system are constructed by using the four PCs from its GS and ES emissions, where the spacing between two nonlinear nodesis very short. These four parallel RCs are potentially applied to address the challenge of high-quality chaos synchronizations. Photon reservoir computing systems utilize the nonlinear dynamics of chaotic lasers to process and predict information [13; 14]. They consist of a chaotic laser, which acts as a \"reservoir\" of nonlinear dynamics, and a readout layer that learns to map the reservoir dynamics to the desired output. This enables the system to capture and utilize the complex dynamics of chaotic signals for various applications [15; 16; 17], including chaos synchronization and prediction. The advantage of photon RC systems lies in their ability to effectively handle the mismatch between the driving laser and the response laser, as well as the variability in their parameters. By utilizing the reservoir dynamics, these systems can adapt and learn from the input chaotic signals, allowing for robust synchronization and separation even in the presence of imperfections and parameter mismatches. In the context of high-speed COCSC, photon RC systems hold great potential for enhancing the synchronization performance and enabling coherent demodulation in multi-channel communication systems. By leveraging the capabilities of photon RC systems, it is expected that the challenges associated with achieving high-quality chaotic synchronization and coherent demodulation can be effectively addressed. Recently, there have been several works proposing a delay-based photon RC system based on electronically pumped spin-VCSELs [15; 18]. This RC system utilizes the nonlinear dynamical x polarization component (X-PC) and Y-PC from the VCSEL output to perform two parallel reservoir computers, which are capable of predicting two independent optical chaotic time-series simultaneously and their synchronizations. The output X-PC and Y-PC from the electronically pumped spin-VCSEL can be interchanged continuously under external perturbations and optical feedback, which can affect the predictive performance of the two parallel RCs. Compared to an electrically-pumped VCSEL, a QD spin-VCSEL offers flexible spin control of the lasing output and provides more control parameters [19; 20]. This enables better controllability for polarization switching and weakly correlated GS and ES dynamics [21; 22]. These advantages allow for the realization of four parallel RCs using the four PCs from the GS and ES emissions of the QD-spin-VCSEL.