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IEEE Wireless Communications and Networking Conference

Entanglement Distribution Over Quantum Networks with Fairness Guarantees

Wenkang Cen, Jinbei Zhang, Kechao Cai, Shi‐Hai Sun

Published Mar 24, 2025• 1 citation
Publisher

Abstract

The entanglement distribution problem over quantum networks has been widely studied, with the objective of maximizing network throughput, that is, the number of entanglements distributed for all user pairs. However, most of the existing works only focus on throughput maximization while neglecting fairness considerations. In this paper, we first characterize the fairness of an entanglement distribution scheme by introducing a fairness factor based on Element-Wise Inequalities, referred to as EWI-fairness. The EWI-fairness requires that the entanglement distribution rate of each user pair exceeds a certain threshold, ensuring the fair distribution. Second, we enforce fairness guarantees into two existing distribution methods, Temporal Multiplexing Distribution (TMD) and Flow Multiplexing Distribution (FMD). Our theoretical analysis reveals that FMD-based scheme outperforms TMD-based scheme. Therefore, we focus on optimizing FMD-based scheme. Third, we formulate the fair entanglement distribution problem as a linear programming problem, where fairness requirements serve as constraints, aiming to identify the optimal FMD-based scheme with the highest throughput. Simulation results demonstrate that the optimized FMD-based scheme achieves a higher throughput compared to existing schemes under identical fairness requirements.

DOI
10.1109/wcnc61545.2025.10978693

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The entanglement distribution problem over quantum networks has been widely studied, with the objective of maximizing network throughput, that is, the number of entanglements distributed for all user pairs. However, most of the existing works only focus on throughput maximization while neglecting fairness considerations. In this paper, we first characterize the fairness of an entanglement distribution scheme by introducing a fairness factor based on Element-Wise Inequalities, referred to as EWI-fairness. The EWI-fairness requires that the entanglement distribution rate of each user pair exceeds a certain threshold, ensuring the fair distribution. Second, we enforce fairness guarantees into two existing distribution methods, Temporal Multiplexing Distribution (TMD) and Flow Multiplexing Distribution (FMD). Our theoretical analysis reveals that FMD-based scheme outperforms TMD-based scheme. Therefore, we focus on optimizing FMD-based scheme. Third, we formulate the fair entanglement distribution problem as a linear programming problem, where fairness requirements serve as constraints, aiming to identify the optimal FMD-based scheme with the highest throughput. Simulation results demonstrate that the optimized FMD-based scheme achieves a higher throughput compared to existing schemes under identical fairness requirements.
Quantum communication networks enable advanced quantum applications through remote entanglement distribution among source-destination pairs. Despite efforts to optimize entanglement distribution, fairness in multi-request scenarios has been neglected, potentially causing issues like “request starvation”. To address such issue, this paper concentrates on the unique properties of entangled systems and introduces a process-oriented fairness metric, i.e., expected throughput, departing from conventional approaches used in classical networks. Furthermore, we propose an entanglement distribution scheme named Fair-EAS, which prioritizes entanglement allocation and selection for batching multiple requests to maximize overall throughput while maintaining max-min fairness. To facilitate a convenient solution, we transform the nonlinearity of the problem into an equivalent linear programming formulation and decouple the solution into offline and online phases. In the offline phase, we design a multi-round water-filling-like optimization algorithm to determine the optimal path set for predicting entanglement allocation. In the online phase, we introduce an adaptive compensation algorithm and an entanglement “fragment” exhaustion algorithm to dynamically adjust the path set based on successfully generated entangled pairs. Comprehensive simulations show that Fair-EAS outperforms the existing schemes in terms of fairness by significantly enhancing the minimum throughput and throughput deviation among multiple requests while maintaining an overall throughput close to the optimal level.
Quantum networks are designed to transmit quantum bits (qubits) among quantum devices to enable new network resources for the applications. Entanglement distribution and entanglement swapping are fundamental procedures that are required in several network operations. However, they are probabilistic operations, which can lead to severe network performance degradation. This article investigates the engineering problem of resource allocation in quantum networks, considering factors like entanglement distribution probability, quantum memory characteristics, and fidelity. We model this as an optimization model to obtain an optimal solution. In particular, we formulate an integer linear programming (ILP) and develop a heuristic algorithm, aiming to minimize the number of required entangled qubit pairs (Bell pairs or EPR pairs) in any adjacent pair in the quantum network. Extensive simulations are performed to compare the performance of proposed ILP and heuristic. In all the cases, the heuristic produces a comparable solution to the optimal one. Simulation results ensure that the value of maximum utilized Bell pairs in a quantum network highly depends on the value of the probability of entangled pairs established, considering the time in the quantum memory besides the number of incoming requests.
Quantum networks offer the capability of transferring quantum information among remote nodes leveraging the phenomenon of quantum entanglement. A key challenge is entanglement routing, which routes quantum entanglement efficiently in a quantum network to satisfy specific objectives. We focus on an interesting hypothesis that arises from the probabilistic nature of quantum entanglement: There is a tradeoff between accommodating a higher number of quantum entanglements (performance) and serving a broader range of node pairs (fairness). To confirm this hypothesis, we formulate entanglement routing as a multi-objective optimization problem. Our numerical analysis reveals that the solutions of the model form a Pareto frontier, thereby validating the hypothesis. Furthermore, we compare the performance of existing algorithms against this Pareto frontier to understand how the algorithms balance performance and fairness. Our findings contribute to designing entanglement routing algorithms.
When built, quantum repeaters will allow the distribution of entangled quantum states across large distances, playing a vital part in many proposed quantum technologies. Enabling multiple users to connect through the same network will be key to their real-world deployment. Previous work on repeater technologies has focussed only on simple entanglment production, without considering the issues of resource scarcity and competition that necessarily arise in a network setting. In this paper we simulated a thirteen-node network with up to five flows sharing different parts of the network, measuring the total throughput and fairness for each case. Our results suggest that the Internet-like approach of statistical multiplexing use of a congested link gives the highest aggregate throughput. Time division multiplexing and buffer space multiplexing were slightly less effective, but all three schemes allow the sum of multiple flows to substantially exceed that of any one flow, improving over circuit switching by taking advantage of resources that are forced to remain idle in circuit switching. All three schemes proved to have excellent fairness. The high performance, fairness and simplicity of implementation support a recommendation of statistical multiplexing for shared quantum repeater networks.
Entanglement distribution in quantum networks must jointly account for limited link capacities, probabilistic entanglement swapping, and heterogeneous link fidelities. In this paper, we study multi-pair fidelity-aware rate allocation in quantum networks. We formulate three rate-allocation problems: rate sum, rate sum subject to minimum-rate constraints, and max-min fairness. Prior work has studied a special case of the rate sum problem, where all links have identical fidelity. This special case admits a polynomial-time algorithm. We prove that all three problems are NP-hard. We then study optimization versions of these problems which maximize the minimum end-to-end fidelity subject to throughput or fairness requirements. We present fully polynomial-time approximation schemes (FPTAS) for solving these optimization problems. Experiments on randomly generated networks demonstrate the computational effectiveness of the proposed schemes.
Quantum networks have emerged as a future platform for quantum information exchange and applications, with promising capabilities far beyond traditional communication networks. Remote quantum entanglement is an essential component of a quantum network. How to efficiently design a multi-routing entanglement protocol is a fundamental yet challenging problem. In this paper, we study a quantum entanglement routing problem to simultaneously maximize the number of quantum-user pairs and their expected throughput. Our approach is to formulate the problem as two sequential integer programming problems. We propose efficient entanglement routing algorithms for these two optimization problems and analyze their time complexity and performance bounds. Evaluation results highlight that our approach outperforms existing solutions in both the number of quantum-user pairs served and network throughput.