Deterministic Entanglement Transmission on Series-Parallel

The performance of entanglement transmission—the task of distributing entanglement between two distant nodes in a large-scale quantum network (QN) of partially entangled pure states—is gen-erally benchmarked against the classical entanglement percolation (CEP) scheme. Improvements beyond CEP were only achieved by nonscalable strategies and for restricted QN topologies. This paper explores and amplifies 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 implement ConPT via a novel 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 DET is designed for general d -dimensional information carriers, scalable and adaptable for any series-parallel QN, and experimentally feasible as tested on IBM’s quantum computation platform. Unlike CEP, the DET mani-fests different levels of optimality for generalized k -concurrences—a fundamental family of bipartite entanglement measures. Our proof also implies that the well-known nested repeater protocol is not optimal for distilling entanglement from pure-state qubits, but the DET is.

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