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We consider the problem of multipath entanglement distribution to a pair of nodes in a quantum network consisting of devices with nondeterministic entanglement swapping capabilities. Multipath entanglement distribution enables a network to establish end-to-end entangled links across any number of available paths with preestablished link-level entanglement. Probabilistic entanglement swapping, on the other hand, limits the amount of entanglement that is shared between the nodes; this is especially the case when, due to practical constraints, swaps must be performed in temporal proximity to each other. Limiting our focus to the case where only bipartite entanglement is generated across the network, we cast the problem as an instance of generalized flow maximization between two quantum end nodes wishing to communicate. We propose a mixed-integer quadratically constrained program (MIQCP) to solve this flow problem for networks with arbitrary topology. We then compute the overall network capacity, defined as the maximum number of Einstein–Podolsky–Rosen (EPR) states distributed to users per time unit, by solving the flow problem for all possible network states generated by probabilistic entangled link presence and absence, and subsequently by averaging over all network state capacities. The MIQCP can also be applied to networks with multiplexed links. While our approach for computing the overall network capacity has the undesirable property that the total number of states grows exponentially with link multiplexing capability, it nevertheless yields an exact solution that serves as an upper bound comparison basis for the throughput performance of more easily implementable yet nonoptimal entanglement routing algorithms. 

Noise and photon loss encountered on quantum channels pose a major challenge for reliable entanglement generation in quantum networks. In near-term networks, heralding is required to inform endpoints of successfully generated entanglement. If after heralding, entanglement fidelity is too low, entanglement purification may be utilized to probabilistically increase fidelity. Traditionally, purification protocols proceed as follows: generate heralded EPR pairs, execute a series of quantum operations on two or more pairs between two nodes, and classically communicate results to check for success. Purification may require several rounds while qubits are stored in memories, vulnerable to decoherence. In this work, we explore notions of optimistic purification, wherein classical communication required for heralding and purification is delayed, possibly to the end of the process. Optimism reduces the overall time EPR pairs are stored in memory, increasing fidelity while possibly decreasing EPR pair rate due to decreased heralding and purification failure. We apply optimism to the entanglement pumping scheme, ground- and satellite-based EPR generation sources, and current state-of-the-art purification circuits that include several measurement and purification checkpoints. We evaluate performance in view of a number of parameters, including link length, EPR source rate and fidelity; and memory coherence time. We show that while our optimistic protocol increases fidelity, the traditional approach may even decrease fidelity for longer distances. We study the trade-off between rate and fidelity under entanglement-based QKD, and find that optimistic schemes can yield higher rates compared to non-optimistic counterparts, with most advantages seen in scenarios with low initial fidelity and short coherence times. 

We study a quantum entanglement distribution switch serving a set of users in a star topology with equal-length links. The quantum switch, much like a quantum repeater, can perform entanglement swapping to extend entanglement across longer distances. Additionally, the switch is equipped with entanglement switching logic, enabling it to implement switching policies to better serve the needs of the network. In this work, the function of the switch is to create bipartite or tripartite entangled states among users at the highest possible rates at a fixed ratio. Using Markov chains, we model a set of randomized switching policies. Discovering that some are better than others, we present analytical results for the case where the switch stores one qubit per user, and find that the best policies outperform a time division multiplexing policy for sharing the switch between bipartite and tripartite state generation. This performance improvement decreases as the number of users grows. The model is easily augmented to study the capacity region in the presence of quantum state decoherence and associated cut-off times for qubit storage, obtaining similar results. Moreover, decoherence-associated quantum storage cut-off times appear to have little effect on capacity in our identical-link system. We also study a smaller class of policies when the switch stores two qubits per user.