# Towards Digital-Twin Assisted Software-Defined Quantum Satellite Networks
## 1 Introduction  
Innovative Quantum Networks (QNs) are conceived with the aim to interconnect multiple Quantum Computers (QCs). The interconnection between multiple QNs will lead, as was the case for the classical Internet, to the creation of a global QN: the so-called Quantum Internet (QI) [1]. In QNs, the created quantum states can be teleported to arbitrarily long distances [2] through the quantum teleportation procedure. In order to perform these operations, pairs of entangled particles are exchanged throughout quantum channels, and classical communication channels are established through the same connections to enable the optimal configuration of the network and transport the information about the quantum teleportation measurements [3, 4, 5, 6, 7, 8]. This network will enable previously unavailable functionalities and also allow for the interconnection of computers with a high level of security. Furthermore, through QI, remote QCs can be interconnected in order to communicate and cooperate with the aim of solving extremely complicated computational tasks operating as a distributed quantum computing system. In fact, the obtained system constitutes a single Quantum Device (QD), which is characterized by a number of qubits that scales linearly with the involved remote QCs and whose computational capacity increases exponentially [1, 9, 10, 11]. However, despite the recent acceleration in the development of quantum technologies, the generation rate of high-fidelity quantum states decreases exponentially with distance due to Optical Fiber (OF) losses [5]. Therefore, performing a large-scale entanglement distribution is still an open issue. To mitigate the transmission problems, it is necessary to introduce specific devices called Quantum Repeaters (QRs). QRs are dedicated devices equipped with Quantum Memories (QMs) that allow for the storage of intermediate quantum states [12]. The whole communication channel is divided by the QRs into several links and the creation of entanglement between neighboring QRs is feasible through the transmission of photons entangled with their QMs. The entanglement swapping procedure is performed between multiple adjacent nodes using specific schemes allowing the generation of the entanglement on an End-to-End (E2E) basis. Specifically, the entangled pairs \(a\) and \(b\) and \(c\) and \(d\) are processed in order to obtain a new Einstein-Podolsky-Rosen (EPR) pair between \(a\) and \(d\), which are not related through entanglement, by conducting a Bell State Measurement (BSM) on particles \(b\) and \(c\). In view of the fact that photons usually experience negligible losses in space vacuum, free-space satellite links have recently been considered as a possible solution for the problems related to OFs, making the transmission of photons over a continental scale feasible. Moreover, QMs and other QR-related devices such as dilution refrigerators have already been tested in the space environment [13; 14], and inter-satellite optical links have been successfully demonstrated in ESA missions [13]. Therefore, the realization of so-called Quantum Satellite Repeaters (QSRs) can be considered feasible [15; 16]. Specifically, as explained in [13; 14], different types of quantum memories exhibit varying storage times. While some have very short durations, others can retain quantum states for up to tens of seconds under specific conditions. Equipping satellites with these advanced memories could allow the storage of entangled pairs until entanglement swapping operations are completed over global-scale E2E satellite communication paths. As reported in [17], LEO satellites, unlike Medium Earth Orbit (MEO) or Geostationary Earth Orbit (GEO) satellites, face unique challenges. These include limited coverage and shorter lifespans due to atmospheric drag. Achieving global coverage with LEO satellites requires the deployment of large constellations, which increases management complexity.