Cost-Aware High-Fidelity Entanglement Distribution and Purification in the Quantum Internet

Operating a quantum network incurs high capital and operational expenditures, which are expected to be compensated by the high value of enabled quantum applications. However, existing mechanisms mainly focus on maximizing the entanglement distribution rate and neglect the cost incurred on users. This paper aims to address how to utilize quantum network resources in a cost-efficient manner while sustaining high-quantity and high-quality entanglement distribution. We first consider how to establish a steady stream of entanglements between remote nodes with the minimum cost. Utilizing a recent flow-based abstraction and a novel graph representation, we design an optimal algorithm for min-cost remote entanglement distribution. Next, we consider distributing entanglements with the highest fidelity subject to a cost bound and prove its NP-hardness. To explore the cost-fidelity trade-off due to swapping and purification, we propose an approximation scheme for maximizing fidelity while satisfying an arbitrary cost bound. Our algorithms provide rigorous tools for supporting high-performance quantum network applications with financial consideration and offer strong theoretical guarantees. Extensive simulation results validate the advantageous performance in cost efficiency and/or fidelity compared to existing solutions and heuristics.