Constant Fidelity Entanglement Flow in Quantum Communication Networks

Entanglement distribution over long distances is one of the main problems in the existing quantum communication networks. Most of the existing methods of establishing entanglement paired link (Einstein, Podolsky, Rosen - EPR pairs) between distant nodes assume symmetric network topologies comprised of links with identical EPR generation capacities. In this work, the entanglement rate capacity of randomly distributed quantum ad hoc networks is investigated. To this end, constant fidelity maximum flow (CFMF) of entanglement problem is defined, and its theoretical analysis is presented. A new heuristic algorithm, i.e., Entanglement Swapping Scheme Search (ESSS), is presented to find the best possible swapping scheme over a multi-hop entanglement path. Furthermore, Shortest Path Entanglement Flow (SPEF) algorithm is introduced as an effective heuristic solution for this problem. Analysis shows that there is a trade-off between the desired constant target fidelity and the entanglement generation rate (maximum flow) of the network.