# _EntangleNet:_ Theoretical Reestablishment of Entanglement in Quantum Networks +
## 2 The Idea of Restoring Entanglement
### General Context
Considering [PERSON] and [PERSON] do not share entangled pairs with each other, but rather each of them does with another node [PERSON], then a quantum relay method achieves teleportation of a qubit from [PERSON] to [PERSON] in two steps: [PERSON] teleports first to [PERSON], followed by him teleporting to [PERSON]. By extension, an arbitrary number of intermediate nodes can exist between [PERSON] and [PERSON], with entangled pairs set up between adjacent stations. This hop-by-hop \"forwarding\" mechanism exhibits an obvious lack of security and privacy [20], as the initial quantum information passes through all the nodes before finally reaching its intended destination. EPR-pair bridging addresses this problem by implementing a swapping scheme that provides [PERSON] and [PERSON] with a shared entangled pair. A Bell measurement performed by [PERSON] on his qubits and a subsequent transmission of classical information will establish entanglement as a particular Bell state between qubits held by [PERSON] and [PERSON]. Using this method based on entanglement swapping, direct teleportation is realized between source and destination. A quantum routing protocol was considered as a combination of quantum relay and EPR-pair bridging mechanisms, without necessary time synchronization between nodes, as a faster completion of operations at source or at the intermediate nodes would degenerate into the former or the latter scheme, respectively [20]. Entanglement swapping is a phenomenon of paramount importance for the entanglement distribution process between two distant nodes. In a most elementary scenario, we consider that there is a node \(O\) halfway between [PERSON] (\(A\)) and [PERSON] (\(B\)) that can generate entangled pairs of particles and then distribute them accordingly. This distribution scheme can be improved, as proposed in [9]. It was demonstrated that a significant speedup is exhibited when further nodes are introduced on the routes \(A-O\) and \(O-B\). Considering [PERSON] and [PERSON] are separated by a distance \(L\) and assuming entangled qubits travel at a speed \(v\), the time required for our parties to receive their qubits generated at \(O\) is no less than \(t_{1}=L/2v\). By placing distribution nodes \(C\) and \(D\) halfway on paths \(A-O\) and \(O-B\), they generate entangled pairs and simultaneously send a qubit to \(O\) and the other one to \(A\) and \(B\), respectively. The time generated qubits require to arrive at their destination nodes is reduced to \(L/4v\). Following a Bell measurement performed at \(O\) that takes \(t_{m}\) to complete, [PERSON] and [PERSON] finally share entanglement. Without accounting for the time necessary for classical information associated with the measurement to be received, then \(A\) and \(B\) are supplied after an interval of \(t_{2}=L/4v+t_{m}\), which is less than \(t_{1}\), provided \(t_{m}<L/4v\). Having analyzed the framework of the problem and several existing protocols, we now continue with presenting our approach to how entanglement can be restored between [PERSON] and [PERSON] in a practical quantum network scenario, improving and generalizing previous results.