Deterministic entanglement distribution on series-parallel quantum networks

The performance of distributing entanglement between two distant nodes in a large-scale quantum network (QN) of partially entangled bipartite pure states is generally benchmarked against the classical entanglement percolation (CEP) scheme. Improvements beyond CEP were only achieved by nonscalable strategies for restricted QN topologies. This paper explores and amplifies a new and more effective mapping of a 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 implement ConPT via a deterministic entanglement transmission (DET) scheme that is fully analogous to resistor network analysis, with the corresponding series and parallel rules represented by deterministic entanglement swapping and concentration protocols, respectively. The main contribution of this paper is to establish a powerful mathematical framework, which is applicable to arbitrary d-dimensional information carriers (qudits), that provides different natural optimality metrics in terms of generalized k-concurrences (a family of fundamental entanglement measures) for different QN topologies. In particular, we conclude that the introduced DET scheme (a) is optimal over the well-known nested repeater protocol for distilling entanglement from partially entangled qubits and (b) leads to higher success probabilities of obtaining a maximally entangled state than using CEP. The implementation of the DET scheme is experimentally feasible as tested on IBM's quantum computation platform.