## 2 Theoretical Framework and Simulation Experiment Setup
The DSPs inscribed with subscripts 4, 9, 14 and 19 adjust and align the clock phase of both transmitter and receiver. The DSPs tagged with the subscripts 5, 10, 15 and 20 are dedicated to estimating and correcting phase discrepancies between the received optical signal and the local oscillator. The BEREMs labeled with subscripts 1-4, as four-dimensional bit error rate modules, are capable of generating \(BER\)s for the baseband signals and facilitating their demodulation. After processing through the four CDUs, four sets of baseband signals (or bit streams) encapsulated within the decoded modulation messages, \(S_{1}^{{}^{\prime}}(t)\), \(S_{2}^{{}^{\prime}}(t)\), \(S_{3}^{{}^{\prime}}(t)\) and \(S_{4}^{{}^{\prime}}(t)\) are effectively reconstructed. These recovered bit streams are denoted as \(b^{1}\)-\(b^{4}\), respectively. Drawing on the spin-flip model (SFM) of vertical-cavity surface-emitting lasers (VCSELs) put forth by [PERSON] et al. [25], the interconnected rate equations characterizing the QD spin-VCSEL\({}_{1}\) (which serves as the driving QD spin-VCSEL) are delineated as follows [19; 26]:\[\frac{dn_{D,WL}^{\pm}}{dt}= \frac{h_{D,2}}{eN_{QD}}[\eta^{\pm}(I_{E,th}-I_{G,th})+I_{G,th}]-\gamma_ {D,0}n_{WL}^{\pm}(\frac{h_{D,2}-n_{DS}^{\pm}}{2h_{D,2}}) \tag{1}\] \[-\gamma_{D,n}n_{WL}^{\pm}\mp\gamma_{D,s}(n_{D,WL}^{+}-n_{D,WL}^{- }),\] \[\frac{dn_{D,ES}^{\pm}}{dt}= \frac{1}{4}\gamma_{D,0}n_{D,WL}^{\pm}(\frac{h_{D,2}-n_{DS}^{\pm}} {h_{D,2}})-\gamma_{D,n}(h_{D,2}+n_{DS}^{\pm})-2\gamma_{D,n}n_{D,ES}^{\pm}|E_{ D,ES}^{\pm}|^{2}\] (2) \[-\gamma_{D,21}(h_{D,2}+n_{D,ES}^{\pm})(\frac{h_{D,1}-n_{D,GS}^{\pm }}{2h_{D,1}})\mp\gamma_{D,s}(n_{D,ES}^{+}-n_{D,ES}^{-}),\] \[\frac{dn_{D,GS}^{\pm}}{dt}= \gamma_{D,21}(\frac{h_{D,2}+n_{D,ES}^{\pm}}{h_{D,2}})(h_{D,1}-n_{ D,GS}^{\pm})-\gamma_{D,n}(h_{D,1}+n_{D,GS}^{\pm})\] (3) \[-2\gamma_{D,n}n_{D,GS}^{\pm}|E_{D,GS}^{\pm}|^{2}\mp\gamma_{D,s}( n_{D,GS}^{+}-n_{D,GS}^{-}),\] \[\frac{dE_{D,GS}^{\pm}}{dt}= k_{D}(n_{D,GS}^{\pm}-1)(1+i\alpha_{D})E_{D,GS}^{\pm}-(\gamma_{D,a}+i \gamma_{D,p})E_{D,GS}^{\mp}+\sqrt{\beta_{sp}}\xi_{D,GS}^{\pm},\] (4) \[\frac{dE_{D,ES}^{\pm}}{dt}= k_{D}(n_{D,ES}^{\pm}-1)(1+i\alpha_{D})E_{D,ES}^{\pm}-(\gamma_{D,a}+i \gamma_{D,p})E_{D,ES}^{\mp}+\sqrt{\beta_{sp}}\xi_{D,ES}^{\pm}. \tag{5}\]  
The interrelated rate equations governing the QD spin-VCSEL\({}_{2}\) (the reservoir QD spin-VCSEL) under the influence of optical feedback and optical injection are revised as follows [19; 26]:  
Figure 2:0 Figure 2:1 (7) Figure 2:2 Figure 2:3 (8) Figure 2:4 (9) Figure 2:5 Figure 2:6 (10) Figure 2:7  
In Equations (1)-(10), the subscript D designates the driving QD spin-VCSEL. The symbols \(+\) and \(-\) represent the right circular polarization (RCP) and left circular polarization (LCP) of the emitted light, respectively. The dynamic variables, indicated by \(n_{WL}\) and \(n_{GS}(n_{ES})\), signify the normalized carrier concentrations in the Wetting Layer (WL) and at the ground (excited) state energy levels. Lasing is facilitated via the transitions from the excited state or the ground state to the valence band (VB), generating right (\(E_{ES}^{+}\), \(E_{GS}^{+}\)) and left (\(E_{ES}^{-}\), \(E_{GS}^{-}\) ) circularly polarized light at two distinct wavelengths. The carrier injection thresholds for the excited and ground states are symbolized by \(I_{E,th}\) and \(I_{G,th}\), respectively. The remaining parameters for the aforementioned QD Spin-VCSELs are as follows: \(k\) and \(k_{D}\) are the photon decay rates; \(\alpha\) and \(\alpha_{D}\) represent the linewidth enhancement factors; \(h_{1}\) and \(h_{D,1}\) are the normalized differential gain coefficients for the ground state transitions; and \(h_{2}\) and \(h_{D,2}\) are those for the excited state transitions.