### Quantum Zeno Dynamics  
Let \(\hat{H}\) be the Hamiltonian acting on a quantum system prepared initially in the \(|1\rangle\) state. Then the probability of finding the system in the same state at time \(t\) is [16]  
\[p(t)=\left|\left\langle e\middle|\exp\left(-\frac{i}{\hbar}\hat{H}t\right) \middle|e\right\rangle\right|^{2}. \tag{5}\]  
Figure 1: Superactivation of bound entanglement (BE) introduced by [PERSON] et al. [13]. (**a**) [PERSON] and [PERSON] are given a Bell state of qubits \(A_{1}\) and \(C_{1}\), but they do not know which Bell state it is. The same state is given to [PERSON] and [PERSON] (qubits \(B_{1}\) and \(D\)), and they do not know which state is given, too. In the same way, pairs [PERSON] and [PERSON], and [PERSON] and [PERSON], are each given an unknown but the same Bell states of qubits \(A_{2}\)–\(B_{2}\) and \(C_{2}\)–\(E\). Both four-qubit systems are BE. (**b**) Following a systematic teleportation procedure, qubits \(D\) and \(E\) are left in a Bell state.  
If the system is subjected to \(n\) projective measurements with sufficiently short intervals \(\tau\), the probability of finding it in the initial state \(p^{n}(\tau)\approx\exp[-(\langle V^{2}\rangle\tau/\hbar^{2})t]\) increases with decreasing \(\tau\), and approaches unity for \(\tau\to 0\)[17]. This shows that carefully designed frequent measurements can slow down the evolution of a quantum system, which is known as the quantum Zeno effect (QZE).  
QZE is promising for protecting a quantum system by slowing down its interactions with its environment [18; 19; 20; 21; 22]. Frequent measurements can also speed up the interaction of a quantum system and its environment, which is known as the anti-Zeno effect [17]. The anti-Zeno effect has been recently attracting attention to improve our understanding of the decay of quantum systems [23; 24; 25; 26] and has been finding interesting applications, such as enabling advantages in quantum heat engines [27]. QZE is also studied in nonlinear systems [28; 29] and is considered to be playing an important role in understanding quantum tunneling [30] and the transition from the quantum to the classical world [31].  
As will be detailed in Section 2, let us consider an iteration step consisting of a set of quantum operations implementing \(\rho\rightarrow\rho^{r}\) and projective measurements implementing \(\rho^{r}\rightarrow\rho^{rmrmrmrmrmrmrmrmrmrmrm  
and  
\[\rho^{rm}=\frac{(J_{0}\otimes J_{0}\otimes J_{0}\otimes I\otimes I)\;\rho^{r}\;( J_{0}\otimes J_{0}\otimes J_{0}\otimes I\otimes I)^{\dagger}}{\text{Tr}[(J_{0} \otimes J_{0}\otimes J_{0}\otimes I\otimes I)\;\rho^{r}\;(J_{0}\otimes J_{0} \otimes J_{0}\otimes I\otimes I)^{\dagger}]}. \tag{9}\]  
Note that the overall rotation operators and threshold measurements with identity operators on the system of eight qubits can be written in a more compact way as \(R(\theta)^{\otimes 6}\otimes I^{\otimes 2}\) and \(J_{0}^{\otimes 3}\otimes I^{\otimes 2}\), respectively, though from the perspective of a quantum network with spatially separated nodes possessing two-qubit systems, we find it more intuitive to write in the form of Equations (8) and (9).  
Similar to the QZD procedure in [32; 33; 34], as the QZD iterations start, the initially separated two-qubit systems become entangled. Because the initially separated qubits held by parties (nodes of the quantum network) [PERSON], [PERSON], and [PERSON] are entangled to qubits in other nodes, as shown in Figure 1a, implementing the local QZD on their initially separable qubits and entangling them, all the eight qubits in the network are entangled without performing teleportation or Bell measurements.  
In the first scenario for distilling a two-qubit entangled state shared by [PERSON] and [PERSON], after a sufficient number of iterations, [PERSON], [PERSON], and [PERSON] measure their qubits on a \(z\)-basis, and communicate the results with [PERSON] and [PERSON].