This paper forms three rate-allocation problems: rate sum, rate sum subject to minimum-rate constraints, and max-min fairness, and presents fully polynomial-time approximation schemes (FPTAS) for solving these optimization problems.
Abstract
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.
As practical quantum networks approach large-scale deployment, the need for efficient user-to-user frequency allocation is increasing, yet current approaches only provide partial solutions to the routing and spectrum allocation problem for an arbitrary quantum network. We address this challenge for repeater-less flex-grid quantum networks based on hyperentangled photons using an efficient three-stage pipeline combining leading tools in classical networking with recent advances in numerical optimization. First, double instantiations of Yen's algorithm obtain low-loss route candidates between each pair of users and the entanglement sources. Second, the advanced process optimizer (APOPT) obtains frequency channel allocations that maximize distribution rates under fidelity constraints. Finally, the constraint programming solver using satisfiability methods (CP-SAT) assigns specific frequency bins to each link, ensuring that there is no contention between frequencies from different sources. We numerically demonstrate this approach on a representative ring network and a Manhattan incumbent local exchange carrier topology, realizing significant improvements over prior genetic algorithm approaches in speed, accuracy, and scalability. Overall, this pipeline provides an efficient heuristic workflow for optimizing broadband entanglement distribution, applicable to arbitrarily connected quantum networks integrated within the existing lightwave infrastructure.
Zachary Goisman, M. L. Stevens, Maxwell Goisman et al.· 0 citations
Quantum network links must distribute entanglement at high rates while satisfying application-specified fidelity demands. However, wide-area deployed fiber links suffer from polarization drift which destabilizes end-to-end fidelity and forces periodic compensation. Current deployments often use active stabilization with fixed control policies, and improvements generally stem from advances in quantum hardware. Meanwhile, software control remains relatively underexplored. Here, we formulate quantum link operation as a joint control problem over tunable rate-fidelity tradeoffs and uncontrollable link drift. From this framework, we construct a link control protocol that dynamically adapts source pump power and polarization compensation to maximize entanglement distribution rate subject to a minimum fidelity constraint. We evaluate the protocol through trace-driven simulations driven by data from a 64 km deployed optical fiber. Compared with optimized static policies, our adaptive controller improves mean entanglement distribution rate by 14% over a 24 hour trace, without requiring any offline policy optimization. Our results show that software-based physical layer control can provide a practical mechanism for improving near-term quantum link performance without requiring additional quantum hardware.
C. Clayton, C. Nunn, Quinn Carmack et al.· 0 citations
In this study, for the first time, a novel routing and purification approach for quantum networks is presented, using the end-to-end (E2E) relative entropy of coherence (REC) together with E2E fidelity to determine the purification level and the feasibility of candidate paths.
H. S. D. Tunç, Joy Halder, Azita Hajizade et al.· Scientific Reports· 0 citations
It is proved that any optimal backbone configuration must correspond to a capacity-maximizing Voronoi tessellation of the network region, and this can be efficiently approximated by a centroidal Voronoi tessellation via Lloyd's algorithm, with backbone nodes connected according to a Delaunay triangulation.
A. Fletcher, Ignazio Pedone, S. Pirandola· 0 citations
End-to-end entanglement distribution in multi-hop quantum networks experiences fidelity degradation as entanglement swapping progresses over noisy and heterogeneous channels. In this paper, we propose a virtual-link purification strategy in which multiple EPR pairs are used at each stage to create virtual links between non-adjacent nodes and then purified in cascade using symmetric purification. The approach allows parameterizing the number of links per stage and follows a hierarchical design, with a more complete first stage and simplified purification in subsequent stages. We implement a time-slot-based orchestrator and compare the proposal against conventional swapping under Werner and bit-flip noise models. The results indicate higher end-to-end fidelity with virtual-link purification.
David Tavares, D. Abreu, Antônio J. G. Abelém· Anais do I Simpósio Brasilei...· 0 citations
We establish operational limits on the broadcasting of genuine multipartite entanglement (GME) in quantum networks. Using a distributed protocol in which each of N parties locally implements optimal 1 $\to$ 2 cloning via beam-splitter interactions, we derive exact expressions for the broadcast fidelity of Greenberger-Horne-Zeilinger (GHZ), W states, and Cluster states in a limited setting. We show that the fidelity decays exponentially with system size as [c(R)]$^N$, providing a quantitative expression of multipartite entanglement monogamy in the broadcasting setting, and that both state families share a universal normalisation factor arising from independent post-selection probabilities. Most significantly, we prove a no-go result for simultaneous GME certification: for all reflectivities and all system sizes, the two broadcast copies cannot be simultaneously certified as genuinely multipartite entangled within the standard framework of fidelity-based witnesses. We further check this behaviour for three- and four-party cluster states, finding consistent results that support the generality of the no-go beyond the GHZ and W families. This obstruction arises from the redistribution of multipartite coherence, which both reduces the achievable fidelity and increases the corresponding certification threshold. Our results reveal a fundamental trade-off between the broadcastability of multipartite entanglement and its operational certifiability, and delineate intrinsic limits on entanglement distribution in quantum networks.