# _EntangleNet:_ Theoretical Reestablishment of Entanglement in Quantum Networks +
## 2 The Idea of Restoring Entanglement  
### General Context  
In a general case of entanglement distribution, [PERSON] and [PERSON] usually have quantum channels connecting them to [PERSON], another node in the network. We refer to [PERSON] as a third party, who might actually represent a laboratory that generates maximally entangled pairs and then sends each particle to [PERSON] and [PERSON], thus having successfully provided them with shared entanglement. Nevertheless, problems arise when considering practical situations of entanglement distribution. Although one ebit constitutes a perfect, noiseless transmission channel for [PERSON] and [PERSON] [10], the entangled pair is still distributed via noisy quantum channels, hence its purity is altered and our parties will eventually share a non-maximally entangled state (less than 1 ebit). By executing the teleportation protocol with such a resource, perfect reconstruction of the original qubit cannot be accomplished. A major result that overcomes these limitations is the process of _entanglement purification_[2; 10], which is possible via local operations. The purpose of purification protocols is to _concentrate_ the entanglement of a certain number of entangled pairs to obtain a higher amount of entanglement for a smaller number of pairs. Given sufficient partially-entangled pairs shared by [PERSON] and [PERSON], under LOCC, they can obtain a pair with entanglement close to 1 ebit in order to teleport a qubit with satisfactory fidelity. Entanglement concentration using nonlinear optics is presented in [11]. Even though entanglement can be concentrated, this process is successful under a minimum fidelity condition for the initial pairs, which cannot be met beyond certain distances [10; 12]. It is reasonable to assume that distances between such arbitrary nodes as those represented by [PERSON] and [PERSON] are significant enough to make this process rather infeasible. This led to the emergence of _quantum repeaters_[12], devices that use _entanglement swapping_[13; 14; 15] and purification in order to propagate entanglement in shorter segments (node to node), until source and destination are linked by an almost maximally entangled pair. Thus, quantum repeaters are key elements in the framework of a quantum network and they have been considered in various entanglement distribution schemes. The phenomenon of entanglement swapping for continuous variables is discussed in [16]. A quantum key distribution scheme involving entanglement swapping is proposed in [17], while a quantum conferencing scheme for secure communication between several users is developed in [18]. An entanglement distribution scheme was recently proposed as an optimal routing protocol that ensures the greatest entanglement distribution rate between two arbitrary nodes in a quantum network [19]. It operates on a graph model of the network, while taking into account physical challenges such as the stochastic nature of entanglement generation, imperfect Bell measurement and short coherence time \(T^{\text{ch}}\) of memories in quantum repeaters. Given multiple possible routes between two nodes, the protocol finds the optimal one according to a route metric. The optimality of the path provides the highest average number of successfully established entangled pairs between two nodes in unit time, considering the coherence time interval \(T^{\text{ch}}\). Through numerical simulations, the underlying algorithm of the protocol was proven to outperform classical graph algorithms (Dijkstra, Bellman-Ford) used in conventional routing. Two other previously proposed routing schemes are referred to as _quantum relay_ and _EPR-pair bridging_[20] (maximally entangled pairs of particles are also called EPR-pairs).