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arXiv:2608.29911

Exact Resource Laws for Passive Wavelength Routing in Entanglement Networks

Ekta Panwar, Gilberto Borges, Saeid Salari, Kartik Kakade, Samgeeth Puliyil, Peter Rapčan, Mario Ziman, Djeylan Aktas

quant-phSubmitted Aug 30, 2026• Announced Sep 1, 2026• 0 citations
v1 · Aug 30, 2026v2 · Oct 22, 2026
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Abstract

Entanglement-based networks provide a scalable framework for multiuser quantum communication by passively routing spectrally correlated photon pairs across interconnected nodes. Several wavelength-allocation schemes have been demonstrated experimentally, but these designs do not yet give a general way to determine how spectral use, receiver load, repeated connections, and fan-out constrain one another. We address this problem through the network's connectivity graph, where the wavelength assignment becomes a resource-optimization problem. For one-sided fan-out, assigning each link to a center and grouping links with the same center gives an exact optimization for arbitrary networks and fan-out limits. We solve this for complete networks and for complete networks in which every user has one excluded partner. Allowing both conjugate wavelengths to fan out changes the resource landscape: a balanced binary hierarchy attains the minimum spectral-layer count for a complete network while reducing the maximum receiver load to logarithmic in the number of users. An eight-user complete network then makes explicit the competing roles of spectral efficiency, receiver load, redundancy, and fan-out. We include the passive-splitter loss and the dependence of the key rate on the delivered pair flux to determine the minimum total pair-generation rate required to meet the prescribed targets. Finally, we formulate the corresponding BBM92 quantum key distribution (QKD) secret-key-rate analysis for a continuous-wave-pumped broadband source, with true and accidental coincidences evaluated between detector channels at the two endpoint users and relative layer pair-generation rates fixed by the source spectrum. This framework, therefore, provides a direct route from exact network resource laws to the design and comparison of passive entanglement architectures under experimentally specified hardware constraints.

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Entanglement-based networks provide a scalable framework for multiuser quantum communication by passively routing spectrally correlated photon pairs across interconnected nodes. Several wavelength-allocation schemes have been demonstrated experimentally, but these designs do not yet give a general way to determine how spectral use, receiver load, repeated connections, and fan-out constrain one another. We address this problem through the network's connectivity graph, where the wavelength assignment becomes a resource-optimization problem. For one-sided fan-out, assigning each link to a center and grouping links with the same center gives an exact optimization for arbitrary networks and fan-out limits. We solve this for complete networks and for complete networks in which every user has one excluded partner. Allowing both conjugate wavelengths to fan out changes the resource landscape: a balanced binary hierarchy attains the minimum spectral-layer count for a complete network while reducing the maximum receiver load to logarithmic in the number of users. An eight-user complete network then makes explicit the competing roles of spectral efficiency, receiver load, redundancy, and fan-out. We include the passive-splitter loss and the dependence of the key rate on the delivered pair flux to determine the minimum total pair-generation rate required to meet the prescribed targets. Finally, we formulate the corresponding BBM92 quantum key distribution (QKD) secret-key-rate analysis for a continuous-wave-pumped broadband source, with true and accidental coincidences evaluated between detector channels at the two endpoint users and relative layer pair-generation rates fixed by the source spectrum. This framework, therefore, provides a direct route from exact network resource laws to the design and comparison of passive entanglement architectures under experimentally specified hardware constraints.
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We investigate resource allocation for quantum entanglement distribution over an optical network. We characterize and model a network architecture that employs a single broadband quasi-deterministic time-frequency heralded Einstein-Podolsky-Rosen (EPR) pair source, and develop a routing and spectrum allocation scheme for distributing entangled photon pairs over such a network. As our setting allows separately solving the routing and spectrum allocation problems, we first find an optimal polynomial-time routing algorithm. We then employ max-min fairness criterion for spectrum allocation, which presents an NP-hard problem. Thus, we focus on approximately-optimal schemes. We compare their performance by evaluating the max-min and median number of EPR-pair rates assigned by them, and the associated Jain index. We identify two polynomial-time approximation algorithms that perform well, or better than others under these metrics. We also investigate scalability by analyzing how the network size and connectivity affect performance using Watts-Strogatz random graphs. We find that a spectrum allocation approach that achieves higher minimum EPR-pair rate can perform significantly worse when the median EPR-pair rate, Jain index, and computational resources are considered. Additionally, we evaluate the effect of the source node placement on the performance.
A fully connected quantum network with a wavelength division multiplexing architecture plays an increasingly pivotal role in quantum information technology. With such architecture, an entanglement-based network has been demonstrated in which an entangled photon-pair source distributes quantum entanglement resources to many users. Despite these remarkable advances, the scalability of the architecture could be constrained by the finite spectrum resource, where O(N^2)wavelength channels are needed to connect N users, thus impeding further progress in real-world scenarios. Here, we propose an optimized scheme for the wavelength division multiplexing entanglement-based network using a state-multiplexing quantum light source. With a dual-pump configuration, the feasibility of our approach is demonstrated by generating state-multiplexing photon pairs at multiple wavelength channels with a silicon nitride microring resonator chip. In our demonstration, we establish a fully connected graph between four users with six wavelength channels - saving half of which without sacrificing functionality and performance of the secure communication. A total asymptotic secure key rate of 1946.9 bps is obtained by performing the BBM92 protocol with the distributed state. The network topology of our method has great potential for developing a scalable quantum network with significantly minimized infrastructure requirements.
Abstract A fully connected quantum network with a wavelength division multiplexing architecture plays an increasingly pivotal role in quantum information technology. With such architecture, an entanglement-based network has been demonstrated in which an entangled photon-pair source distributes quantum entanglement resources to many users. Despite these remarkable advances, the scalability of the architecture could be constrained by the finite spectrum resource, where O(N2){\mathscr{O}}\left({N}^{2}\right)O(N2) O N 2 wavelength channels are needed to connect N users, thus impeding further progress in real-world scenarios. Here, we propose a scheme for the wavelength division multiplexing entanglement-based network using a state-multiplexing quantum light source. With a dual-pump configuration, the feasibility of our approach is demonstrated by generating state-multiplexing photon pairs at multiple wavelength channels with a silicon nitride microring resonator chip. In our demonstration, we establish a fully connected graph between four users with six wavelength channels—saving half of which without sacrificing functionality and performance of the secure communication. A total asymptotic secure key rate of 1946.9 bps is obtained by performing the BBM92 protocol with the distributed state. The network topology of our method has great potential for developing a scalable quantum network with significantly minimized infrastructure requirements.
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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.