We perform a numerical optimisation of the hardware parameters of an atomic-ensemble-based single repeater setup. The setup operates on a real-life fiber network connecting the cities Delft and Eindhoven. Besides this network, the setup encompasses photon pair sources, quantum memories, single photon detectors, and 50:50 beam splitters. The corresponding hardware parameters we consider are the following;
- The detector efficiency, defined as the probability the photon detector correctly registers an incident photon.
-The detector dark count probability, defined as the probability that a detector registers a false detection event.
- The memory efficiency, defined as the maximum probability that an excitation is not lost in the quantum memory.
- The memory coherence time, defined as the characteristic time after which an excitation is lost in the quantum memory.
- The Hong-Ou-Mandel visibilty, which is a measure of the indistinguishability of the photons in the setup.
Additionally, the setup has the ability to be multiplexed. This means that the probabilistic processes essential for executing the repeater protocol are initiated $M$ times in parallel. This increases the performance of the protocol.

To achieve the optimisation, we introduce absolute minimal hardware requirements and minimal hardware requirements. An absolute minimal hardware requirement is defined as the least favourable hardware parameter that still allows the setup to reach a given target metric. This implies that all other hardware parameters are at their optimal value. Minimal hardware requirements are defined as the least favourable set of hardware parameters that still allow the setup to reach a given target metric.

To evaluate the aforementioned target metric we conduct a numerical analysis. This analysis is based on the entanglement based version of quantum key distribution. We use Netsquid, a discrete event simulator for quantum networks, to carry out the numerical analysis. Utilising this, we formulate an optimisation problem that allows us to find absolute minimal hardware requirements and minimal hardware requirements for an atomic-ensemble-based single repeater setup.

We develop a method to solve this optimisation problem. This allows us to find absolute minimal hardware requirements and minimal hardware requirements for the hardware parameters listed above. We do this for different number of multiplexing modes, and different node placements on the existing fiber network. We consider both perfect photon pair sources and a model of a photon pair source based on Spontaneous Parametric Down Conversion (SPDC).

Entanglement is an essential resource for a variety of applications, such as distributed quantum computing and quantum cryptography. However, long-distance entanglement generation is challenging because of two reasons: photon loss occurs as an exponential function of distance through an optical fiber and the no-cloning theorem prevent us from directly amplifying the photons. Therefore, quantum repeaters that enable long-distance communication to realize quantum information-based protocols are desired. One way to achieve a higher entanglement generation rate is to make many attempts of generating entangled states in parallel, a process known as time-multiplexing. There has been previous work investigating the performance of time-multiplexed entanglement generation using processing nodes, but only at the elementary link level. Furthermore, this analysis was restricted to the rate of entanglement generation, with no concern for the fidelity. In this work, we go further by investigating both the fidelity and the rate of entanglement generation of time-multiplexed protocols by analyzing the secret key rate (SKR) of quantum key distribution. Moreover, we also study setups with one and two repeaters. Specifically, we investigate the impact of different hardware parameters on the SKR. Among other results, we conclude that swap gate time is a key factor for achieving higher SKR. We also examine what effect different repeater-chain protocols have on the performance of repeater chains with limited hardware resources. We find that having the repeater send photons in alternating fashion towards both end nodes results in a higher SKR than generating entanglement sequentially. Besides, we investigate what is the most efficient distribution of communication qubit (CQ) in a protocol with multiple repeaters. We ascertain that the repeater chain setup in which the number of CQs in a node is equal to that node's number of neighbors makes best use of its resources.

Distribution of high-quality entanglement over long distances is a key step for the development of a future quantum internet. Exponential photon loss related to distance in optical fibres makes it impractical to connect two nodes directly. Furthermore, the impossibility of copying general quantum states forbids using the same solutions as in classical communication. Quantum repeaters can be used to extend entanglement to longer distances using teleportation; nonetheless, straightforward application still leads to an exponential decrease in the link quality. Entanglement purification probabilistically allow us to obtain few high-quality links from many low-quality ones. Several protocols combining quantum repeaters with purification have been proposed. However, the hardware quality is still lacking. Moreover, it is unclear how an improvement over a certain hardware parameter affects the final link quality or entanglement generation rate. Analytical expressions are hard to find and usually assumptions are needed, limiting their applicability. In this work, a realistic repeater chain is modelled using NetSquid, a discrete-event based quantum network simulator. A genetic algorithm-based optimisation methodology is then applied to determine what entanglement distribution protocol allows for minimal improvement over current hardware, and what these improvements must be in order to achieve a target link quality and distribution rate. In this thesis, we aim to make the path towards scalable quantum repeaters clearer, as well as understand how entanglement purification can enable this goal. We conclude that quantum repeaters are necessary to connect distances larger than 200km. We also find that entanglement purification enables achieving target metrics with lower hardware cost when the internode distance is approximately 100km, where a balance is found between a low rate for longer separations and a too demanding hardware for shorter ones. Finally, we analyse the growth of the hardware cost with the distance showing that, with the best choice of protocols, it scales linearly. We believe that these results constitute a valuable stepping stone towards a blueprint for a pan-European quantum internet.