The unbreakable security and higher data rates offered by quantum communication networks have made quantum communication an inevitable necessity of the future. Many quantum communication frameworks, such as quantum key distribution and super dense coding, require entangled pairs to be shared between the source and destination nodes. Communication nodes in quantum networks have a minimum fidelity requirement for the entangled pairs. If the fidelity requirement is not satisfied, the entangled pairs may not be used for the desired operations. Successful sharing of the entangled pairs between the nodes is a crucial step in making quantum communication practical. In this work, we propose a framework to maximize entanglement sharing between a source and multiple destination nodes in a fair manner. We consider a system that takes advantage of the purification process to improve the fidelity of the entangled pairs when necessary. The proposed solution framework provides the optimal number of entangled pairs required for the purification process and the optimal transmission rate at the source node to achieve the desired system objective. The non-convex problem is first transformed into a convex form, and then a Lagrangian dual-based framework is proposed to find the optimal solution values. Moreover, to optimize the number of entangled pairs for purification at each link, we derive a closed-form expression that provides the optimal value in a single step. Selected simulation results demonstrate that the proposed framework exhibits excellent performance.
The unbreakable security and higher data rates offered by quantum communication networks have made quantum communication an inevitable necessity of the future. Many quantum communication frameworks, such as quantum key distribution and super dense coding, require entangled pairs to be shared between the source and destination nodes. Communication nodes in quantum networks have a minimum fidelity requirement for the entangled pairs. If the fidelity requirement is not satisfied, the entangled pairs may not be used for the desired operations. Successful sharing of the entangled pairs between the nodes is a crucial step in making quantum communication practical. In this work, we propose a framework to maximize entanglement sharing between a source and multiple destination nodes in a fair manner. We consider a system that takes advantage of the purification process to improve the fidelity of the entangled pairs when necessary. The proposed solution framework provides the optimal number of entangled pairs required for the purification process and the optimal transmission rate at the source node to achieve the desired system objective. The non-convex problem is first transformed into a convex form, and then a Lagrangian dual-based framework is proposed to find the optimal solution values. Moreover, to optimize the number of entangled pairs for purification at each link, we derive a closed-form expression that provides the optimal value in a single step. Selected simulation results demonstrate that the proposed framework exhibits excellent performance.
Abstract We address the problem of efficiently distributing high-fidelity entangled states across the nodes of a quantum network—a fundamental requirement for quantum communication, distributed quantum computing, and emerging quantum internet applications. We consider a repeater-based architecture that combines entanglement swapping (or fusion) with purification operations, which enhance fidelity by consuming additional entangled pairs. While prior work has explored routing and limited purification strategies, we present the first algorithms for fidelity-constrained entanglement distribution that are near-optimal and compatible with arbitrary purification models. Our approach introduces the notion of purification-augmented entanglement trees, and we develop dynamic programming (DP) algorithms to construct such trees that maximize the generation rate of entangled pairs (EPs) under fidelity constraints. We further extend our framework to a linear programming (LP)–based flow model that enables simultaneous generation of EPs across multiple source-destination pairs. For multipartite entanglement, we generalize our methods to GHZ and arbitrary graph states, supported by novel analytical models for fidelity evolution under fusion and purification. We evaluate our techniques using the NetSquid quantum network simulator and observe consistent performance improvements over prior approaches—achieving an average 50\% increase in generation rate, and up to 100-150\% in some scenarios.
Entanglement routing establishes remote entanglement connection between two arbitrary nodes, which is one of the most important functions in quantum networks. The existing routing mechanisms mainly improve the robustness and throughput facing the failure of entanglement generations, which, however, rarely include the considerations on the most important metric to evaluate the quality of connection, entanglement fidelity. To solve this problem, we propose purification-enabled entanglement routing designs to provide fidelity guarantee for multiple Source-Destination (SD) pairs in quantum networks. In our proposal, we first consider the single S-D pair scenario and design an iterative routing algorithm, Q-PATH, to find the optimal purification decisions along the routing path with minimum entangled pair cost. Further, a low-complexity routing algorithm using an extended Dijkstra algorithm, Q-LEAP, is designed to reduce the computational complexity by using a simple but effective purification decision method. Then we consider the common scenario with multiple S-D pairs and design a greedy-based algorithm considering resource allocation and rerouting process for multiple routing requests. To verify the effectiveness and superiority of the proposed algorithms, extensive simulations are conducted, and the simulation results show that the proposed algorithms not only can provide fidelity-guarantee routing solutions, but also has superior performance in terms of throughput, fidelity of end-to-end entanglement connection, and resource utilization ratio, compared with the existing routing scheme.
Entanglement routing establishes remote entanglement connection between two arbitrary nodes, which is one of the most important functions in quantum networks. The existing routing mechanisms mainly improve the robustness and throughput facing the failure of entanglement generations, which, however, rarely include the considerations on the most important metric to evaluate the quality of connection, entanglement fidelity. To solve this problem, we propose purification-enabled entanglement routing designs to provide fidelity guarantee for multiple Source-Destination (S-D) pairs in quantum networks. In our proposal, we first consider the single S-D pair scenario and design an iterative routing algorithm, Q-PATH, to find the optimal purification decisions along the routing path with minimum entangled pair cost. Further, a low-complexity routing algorithm using an extended Dijkstra algorithm, Q-LEAP, is designed to reduce the computational complexity by using a simple but effective purification decision method. Finally, we consider the common scenario with multiple S-D pairs and design a greedy-based algorithm considering resource allocation and re-routing process for multiple routing requests. Simulation results show that the proposed algorithms not only can provide fidelity-guaranteed routing solutions, but also has superior performance in terms of throughput, fidelity of end-to-end entanglement connection, and resource utilization ratio, compared with the existing routing scheme.
Quantum communication technology provides an absolute security guarantee for information transmitted between quantum applications. To establish practical quantum networks, providing entangled pairs of stable quality, suitable for varying distances, is crucial. However, due to the inherent losses and imperfections of the operations during the entanglement distribution process, the fidelity of end-to-end entangled pairs will be greatly reduced. Consequently, establishing fidelity-guaranteed entangled pairs will be challenging. In this work, we introduce an entanglement distribution method that ensures the fidelity requirements of applications across different distances, while maintaining high efficiency. The method first decomposes the end-to-end fidelity requirements to target fidelity for purification at each link, based on the worst-case consumption. Then it performs multiple-round symmetrical entanglement purification based on the backup scheme to purify each entangled pair to the target value. The experimental results indicate that the scheme has acceptable performance in resource consumption and great feasibility while ensuring high efficiency.
Entanglement-based quantum networks provide unconditionally secure quantum communication by distributing end-to-end entangled pairs. To reach such goal, entanglement swapping and purification are two necessary operations, which can expand the entanglement distance and improve the fidelity of entangled pairs, respectively. During the end-to-end entanglement distribution process, the execution sequence of these two operations has a significant impact on the final performance, such as throughput and fidelity. Thus, how to schedule the sequence of swapping and purification becomes a critical problem in quantum networks. Our work focuses on such scheduling problem and we devise an efficient solution with fidelity maintenance. In our article, we first propose a concurrent swapping method for any-length path to reduce delay. Secondly, by modeling the scheduling sequence as a permutation problem, we obtain an optimal scheduling principle called “prioritized purification (PP)”. Finally, to meet the fidelity requirement of the end-to-end entangled pairs, we propose a fidelity maintenance scheme based on PP (FMSPP). The simulation results show that the proposed FMSPP can achieve higher distribution rates and less resource overhead than other scheduling solutions, and the advantages are more significant when there are more hops on the path.
This paper studies reliable teleportation of quantum bits (called qubits) in a quantum data network with multiple sources (S) and destinations (D) as well as repeaters. To teleport qubits for a SD pair reliably, not only an entanglement path for the SD pair, but also appropriate purification of the links along the path is required to ensure that the end-to-end (E2E) fidelity of the established entanglement connections is high enough.This is the first work on quantifying the E2E fidelity, and also using this E2E fidelity to determine critical links to achieve the most resource efficient purification. A novel approach called E2E Fidelity aware Routing and Purification (EFiRAP) is proposed to maximize network throughput, i.e., the number of entanglement connections among multiple SD pairs, with each connection having an E2E fidelity above a given required threshold. EFiRAP accomplishes this goal by first preparing multiple candidate entanglement paths and determining optimal purification schemes, and then selecting the final set of entanglement paths that can maximize network throughput under the given quantum resource constraints. Existing works only ensured the fidelity of individual links, rather than the E2E fidelity is above a given threshold. Extensive simulations show that the proposed EFiRAP can enhance network throughput by about 50% when compared with the state-of-the-art approach.