## 3 Results
### Scenario 2  
Our second scenario is to superactivate bound entanglement by entangling all the qubits in the nodes of the given quantum network, as illustrated in Figure 5, via QZD. Note that the blue lines connecting qubits do not imply a cyclic entanglement, they only show that every qubit is entangled. The obtained free entangled state of the eight-qubit system is not a GHZ or W state, but it can be considered a generic graph state. Unlike the first scenario and the original superactivation [13], where a two-qubit entangled state is obtained, the eight-qubit bound entangled state, we show that an eight-qubit genuine multiparticle entanglement can be obtained. Moreover, because no qubit is measured on a \(z\)-basis, our second scenario is free from the probabilistic results, which enables the superactivation to have a significantly smaller number of iterations. Distillable entanglement in the eight-qubit system requires inseparability among all bipartite cuts. In the initial state \(\rho\), the \(\rho_{4:4}\) cut is separable, i.e., \(m:=\min_{i}(LN(\rho_{i:8-i}))=0\). Then the question turns to find a QZD procedure achieving \(m>0\). Not surprisingly, it is straightforward to show that implementing the proposed QZD procedure, \(m>0\) can be easily obtained. We plot the results of our numerical simulations up to 700 iterations in Figure 7, and the maximum \(m\) is achieved in 611 iterations with \(m\approx 0.86\). The logarithmic negativity of all bipartite cuts of \(\rho^{611}\) is found as \(\{0.99429,1.9038,1.3436,0.8581,1.2888,1.9831,0.99867\}\). While \(\sum_{i}LN(\rho_{i:8-i})=8\), achieving a greater value would show that QZD increases the amount of total entanglement in the network. Therefore, we plot in Figure 8 the sum of logarithmic negativity values of bipartite cuts of the system throughout the QZD procedure and find that \(\sum_{i}LN(\rho_{i:8-i}^{611})=9.37\). By implementing QZD, this result shows that as an EPR pair was obtained out of two separable qubits in [32] and entanglement swapping was achieved by entangling initially separable qubits in [33], the procedure proposed herein both superactivates bound entanglement and also increases the total entanglement in terms of the sum of entanglement of bipartite cuts. In order to confirm that no bipartite cut of \(\rho^{611}\) is separable in that writing, we also rewrite it in the same order of qubits, i.e., \(A_{1}C_{1}B_{1}DA_{2}B_{2}C_{2}E\) as in \(\rho_{init}\) and denote it \(\sigma\). Then we find \(LN(\sigma_{i8-i})=\{0.99429,0.56478,1.16463,0.52604,1.17306,0.62304,0.99869\}\) for \(i=0,1,..,8\) with \(m\approx 0.526\). We further detail our analysis on \(\sigma\) by investigating the inseparability of its subsystems. We first trace out the first and the last four qubits of \(\sigma\), respectively, and calculate the logarithmic negativity of bipartite cuts of the remaining subsystem. Due to the symmetry of the system, for both subsystems, we find  
\[LN(tr_{A_{1}C_{1}B_{1}D}(\sigma)_{i:4-i})=LN(tr_{A_{2}B_{2}C_{2}E}(\sigma)_{i: 4-i})=\{0.82073,0.105191,0.821025\} \tag{17}\]where \(i=0,1,2,3,4\). In both scenarios above and, in general, in QZD, the idea of the threshold measurements is that throughout the iterative process, the probability \(\epsilon\) that the system collapses to the inhibited subspace is very small and the probability that the system continues its evolution in the uninhibited subspace upon successful projection to it is close to unity. However, in reality, an arbitrary \(\epsilon\) depending on the initial state and chosen threshold operators is observed in the first iteration, which then approaches unity throughout the  
Figure 8: Sum of logarithmic negativity of bipartite cuts of the eight-qubit system throughout QZD, i.e., \(\sum_{i}LN(\rho_{i8-i}^{n})\). Because this sum is initially equal to 8, yet the entanglement is nondistillable, achieving a greater value shows that in addition to superactivating bound entanglement, our QZD procedure increases the amount of entanglement of the quantum network.