Performance of processing-node repeaters with time-multiplexed entanglement generation

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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.