## 4 Discussions  
Although the result in Scenario 1 is not the major contribution of our work and we considered it only to show that the original superactivation of bound entanglement by [PERSON] et al. in [13] can be realized by leaving two-qubit distillable entanglement via QZD, is worth discussing its drawbacks in detail. Following \(n\) iterations, the first three pairs of qubits, each possessed by [PERSON], [PERSON], and [PERSON], are measured on a \(z\)-basis. Because QZD is inhibiting the subspace \(\ket{1}\otimes\ket{1}\) for each pair, and the evolution of the system takes place in the uninhibited subspace; the \(z\)-measurements have 63 possible outcomes with probabilities oscillating around \(1/63\) throughout the evolution. The result we presented achieving \(LN(\rho_{DE}^{3345})\approx 0.8\) is for the outcome \(\ket{0}^{\otimes 6}\). Superactivation is actually observed in several outcomes with almost all \(n>0\), though achieving smaller logarithmic negativity. Figure 9: Sum of logarithmic negativity of all bipartite cuts of the eight-qubit system throughout QZD with three choices for greediness, \(t=1\), \(t=5\), and \(t=10\), as explained in the flowchart of the algorithm in Figure 6. The greediest choice \(t=1\) performs the best, driving the system to a maximally entangled state with \(\sum_{i=1}^{7}LN(\sigma_{i8-i})\approx 16\) in only around 300 iterations. However, for the proof of concept in Scenario 1, we considered a simple QZD procedure with the same threshold measurement operator \(J_{0}\) and single-qubit rotation angle \(\theta\) for all the parties and all the iterations. In [32], for creating entanglement between initially separable two qubits via QZD, [PERSON] et al. were able to find an intelligent evolution strategy after 100 iterations; they implement a single-qubit quantum operation followed by another 50 iterations, which improves the overall procedure. As also discussed by [PERSON] et al. in [33], due to the size of the parameter search space, a brute force approach for finding an optimal set of measurement operators and rotations for each iteration is not feasible, requiring artificial intelligence (AI) techniques. Finding an optimal parameter set, the final distillable two-qubit entanglement could be made even closer to a maximally entangled Bell state. More importantly, if it could be obtained regardless of the outcome of \(z\)-basis measurements, then after implementing QZD, the first six qubits can be simply traced out, also eliminating the final classical communications for the outcomes. Therefore, we point out developing a quantum AI-based search strategy for improving the proposed QZD procedure. Scenario 2 is free from \(z\)-measurements, and in addition to superactivation bound entanglement, it increases the total amount of entanglement among the eight-qubit quantum network in terms of bipartite cuts. Further, a significantly smaller number of iterations is sufficient to obtain these results. Nevertheless, it would benefit from such an intelligent evolution, too. More importantly, in this work, we have not considered a particular class of quantum network such as GHZ [1], W [39], or a generic unweighted [40] and even weighted [41] graph state for one-way quantum computation. Therefore, quantum AI strategies could help generate multipartite entangled systems in particular classes via QZD. As the second major contribution of this work, we designed a universal optimization algorithm with variable greediness that can be applied to QZD evolution in both qubit systems, such as in [32,34], and higher dimension systems, such as in [33], with an arbitrary number of particles. We implemented the algorithm for the present setting and showed that while the raw (un-optimized) evolution can increase the entanglement from \(\sum_{i}LN(\rho_{i\delta-i}^{n})=8\) to \(\approx 9.4\) in 700 iterations, the optimization algorithm can increase it up to 16, the maximum value in only around 300 iterations. This algorithm aimed to increase the entanglement of the system.