Deterministic Entanglement Transmission on Series-Parallel Quantum Networks

The performance of entanglement transmission---the task of distributing entanglement between two arbitrarily distant nodes in a large-scale quantum network (QN)---is generally benchmarked against the classical entanglement percolation (CEP) scheme. Up to now, improvements of entanglement transmission beyond CEP have only been achieved, with great loss of generality, by nonscalable strategies and/or for restricted QN topologies. This talk explores a new and more effective mapping of QN, referred to as concurrence percolation theory (ConPT), that suggests using deterministic rather than probabilistic protocols for scalably improving on CEP across arbitrary QN topology. More precisely, we introduce a novel implementation of the ConPT mapping via a deterministic entanglement transmission (DET) scheme that is fully analogous to calculating the total resistance in resistor circuits, with the corresponding series and parallel rules represented by specific deterministic entanglement swapping and purification protocols, respectively. The DET is designed for general d-dimensional information carriers and is scalable and adaptable for any series-parallel QN, as it reduces the entanglement transmission task to a purely topological problem of calculating path connectivity. Unlike CEP, the DET displays different levels of optimality for generalized k-concurrences---a fundamental family of measures of bipartite entanglement---on different QN topologies. More interestingly, our work implies that the well-known nested purification repeater protocol does not optimize the final concurrence, a result that essentially relies on a special reverse arithmetic mean--geometric mean (AM--GM) inequality.