# _EntangleNet:_ Theoretical Reestablishment of Entanglement in Quantum Networks +
## 1 Introduction  
Quantum teleportation is a communication protocol introduced by [PERSON] et al. [1] and represents a major result in the field of quantum information. It allows perfect transmission of an unknown qubit between two spatially separated parties (whom we shall call [PERSON] and [PERSON]), provided that classical information is exchanged and a previously shared maximally entangled pair of particles exists between them [1; 2; 3]. Quantum entanglement is one of the most peculiar aspects exhibited by nature and an essential resource for teleportation. Shared maximal entanglement is required to achieve faithful teleportation; however, an inherent limitation is that this highly valuable resource is lost afterwards. In such context, shared entanglement as an informational resource is expressed in a quantitative manner as one _entanglement bit_ or \(1\)_ebit_[2, 4]. The teleportation scheme is part of a paradigm known as _local operations and classical communication_ (LOCC), with additional shared entanglement allowed. This means that [PERSON] and [PERSON] share an entangled pair of particles, can manipulate their own qubits at will (LO) and can only exchange classical bits of information (CC). An important drawback of the protocol is closely related to properties of entanglement under LOCC; specifically, one shared ebit is necessary for faithful teleportation and the amount of shared entanglement cannot be increased by local operations and classical communication [2, 4; 5; 6; 7; 8]. A consequence of these constraints is the consumption of one shared ebit when teleporting one qubit, thus entanglement between [PERSON] and [PERSON] is lost.  
Alice and Bob are thought to be part of an extended quantum network infrastructure, with quantum channels providing communication links between adjacent nodes. Physical transmission of particlesthrough these inherently noisy channels will definitely alter the encoded quantum information they wish to exchange. Teleportation proves to solve this problem by accurately transmitting a qubit from one place to another, regardless of distance and without any physical transport. However, it requires a maximally entangled pair of particles to be shared between source and destination; therefore, a crucial aspect of a future large scale quantum network is the task of reliably distributing entanglement to any two nodes in need of exchanging quantum information via teleportation.  
We have chosen to devise a theoretical entanglement distribution protocol based on quantum routing that manages to resupply any two nodes [PERSON] and Bob in a quantum network with shared entanglement. Our result is a generalization of [9] that reduces the entanglement distribution time by a factor of \(4k\) relative to direct transmission of entangled qubits, considering a number of \(4k-1\) specifically chosen quantum nodes between source and destination, as detailed in Section 2.2.  
This paper is organized according to the following structure. In Section 2, we explore the process of entanglement distribution in quantum networks and discuss already established results. Then, we present our idea that improves and generalizes previous results, along with a resource analysis regarding the time needed to supply the end nodes with a maximally entangled pair of qubits. In Section 3, we provide an algorithmic description of the protocol and in Section 4 we conclude with final remarks and discuss future work.