Asynchronous Routing for Multipartite Entanglement in Quantum Networks

Published in the 2026 IEEE 16th Annual Computing and Communication Workshop and Conference (CCWC), Las Vegas, NV, USA, 2026 , pp. 053 3 - 0541, doi: 10.1109/CCWC67433.2026.11393739. Asynchronous Routing for Multipartite Entanglement in Quantum Networks C henliang Tian Department of Comp uter Sc ience a nd Engineering Washi ngto n Uni vers ity St. Louis, USA chenliang.t@wustl.edu R amana K om pella Quantum Lab Cisco Santa Monica, USA rkompell@cisco.co m A iman E rbad Department of Comp uter Sc ience a nd Engineering Qatar Uni versit y Doha, Qat ar aerbad@qu.edu.qa Zebo Yang Department of El ectric al Engi neering and Computer Science Florida Atlanti c University Boca Raton, USA yangz@fau.edu Reza Nejaba ti Quantum Lab Cisco Santa Monica, USA rnejabat@cisco.com M ounir H amdi Department of Sc ience an d Engine ering Hamad Bin Khalifa Univers ity Doha, Qat ar mhamdi@hbk u.edu. qa Raj Jain Department of Comp uter Sc ience a nd Engineering Washi ngto n Uni vers ity St. Louis, USA jain@wustl.edu E neet K aur Quantum Lab Cisco Santa Monica, USA ekaur@cisco.com Mohamed Abdal lah Department of Sc ience an d Engine ering Hamad Bin Khalifa Univers ity Doha, Qat ar moabdall ah@hbku .edu.q a Abstract — In quantum networks, one way to com municate is to distribute entanglem ents through swap ping at intermediate nodes. Most existing w ork primarily aims to creat e eff icient two - party end - to - end entanglement over long distances. However, some scenarios also req uire remote multipartite entanglement for applications such as quantum secret sharing and multi - party computation. Our previous study improved end - to - end entanglement rates using an asynchronous, tree - based routing scheme that relies solel y on loc al knowledge of e ntanglement links, conserving unuse d entanglement and avoiding synchronous operations. T his article ext ends this approach t o multip artit e entang lement s, parti cular ly the thr ee - party Greenberg er - Horne - Zei linger (GHZ) states . It shows that our asynchronous protocol outperforms traditional synchronous methods in entanglement rates , especially as coherence ti mes increase. This approach can also be extended to four - party and larger multipartite GHZ states, highlighting the effectiveness and adaptability of asynchronous routing f or multipartite scenarios across vario us network topologies . Keywords — Entanglemen t Distribut ion, Multip artite Entanglement , Quant um Routi ng, Quan tum Netwo rk, Qua ntum Internet, Quantum Repeater. I. I NTRODUCTION The emergence of quantum computing has heralded new advancements in communication networks [1] . Rooted in quantum mechanics, quantum networks off er enhanced security and computational capabilities beyond those of classical systems. Key applications include quantum key distribution (QKD), distributed quantum computations, and quantum teleportation [2] . A key requir ement for these technologie s is est ablishing remote entanglement over long distances. Quantum repea ters have been developed to tackle the issue of long - distance quantum entanglement degradation [3] . These repeaters utilize entanglement swapping and fusion measurements to facilitate two - party and multipartite ent anglement [4] [5] [6] . Such technol ogy extends entanglement across multiple repeaters, creating long - distance end - to - end or multi - party connections. Fig. 1. Illustration of swapping and G HZ fusion. Existing entanglement routing schemes — commonly referred to as synchronous or two - phase protocols — typically consist of two main phases: the ent anglement generation phase and the entanglement distribution phase [4] [5] [6] [7] . The generation phas e creates entang lement between dir ectly connected quantum nodes through quantum operations on their qubits, forming a primary layer of entangled pairs acro ss adjacent nodes – often called instant topology. In contrast, the underlying n etwork of optical links is known as the physical topology. T his phase establishes the foundational links or building blocks for broader network - wide entanglement s. Once t he in stant topology is e stablished, th e dis tribution phase begins, aiming to extend en tanglements across the network to nodes t hat ar e not dir ectly connected. This phase involves entanglement swapping and fusion measurements, as shown in Fig. 1 , with Fig. 1 (b) illustrating a three - party Greenberger – Horne – Zeilinger (GHZ) state as an example. These processes allow connecting two or more entangled pairs via an Swapping at the repeater End- to -end entanglement GHZ fusion at the repeater Three-party GHZ stat e Qubit Direct-link entanglement Three-party GHZ fusion Entanglement swapping This work was suppor ted in part by Cisco University Re search Grant #98690499 and the Qatar Research, Development, and Innovation (QRDI) Academic Rese arch Grant #ARG02 - 0415 - 240191 . The statements mad e here are solely the re sponsibility of the authors. Published in the 2026 IEEE 16th Annual Computing and Communication Workshop and Conference (CCWC), Las Vegas, NV, USA, 2026 , pp. 053 3 - 0541, doi: 10.1109/CCWC67433.2026.11393739. intermediate node, effectively linking distant nodes with in the network. These two phases are typically performed in synchronized time slots under global link - state knowledge, where each repeater knows which direct - link entanglements succeeded after the generation phase. This allows centralized pat h selection for swapping or fusion during the distribution phase. To ens ure t he availability of fresh direct - link entanglement for each distribution phase, these synchronous protocols typically reset the netw ork state at the end of every tim e slot and repeat the two - phase cycle in the next one. Each complete run of the two phases is considered a single timeframe. If, within a given timeframe, no connected path exists between the request nodes or if swapping or fusion att empts fail to establish end - to - end entangl ement, the network advances to t he next synchronous round, and the entire process is repeated. Although this global synchronizatio n ensures, the repeated rests deplete the available entanglement with in each timeframe, resulting in a low er end - to - end entanglement rate. To address these li mitations, we deve loped a family of asynchronous entanglement routing (AER) protocols i n [8] and [9] that improve th e end - to - end throughput and allow rates to scale with extended coherence times, outperforming synchronized methods. AER uses instant topology in a fully distributed manner, eliminating the need for synchr onization . This instant topology generall y forms a tree - like configuration, such as a dest ination – oriented directed acyclic graph ( DODAG) [10] . Similar structures have been well researched in the context of classical lossy wireless networks, which also experience connection lo sses . In a quantum setting, this corresponds to entanglement loss in the instant topology, with the loss probabili ty dete rmined by both the ph ysical link quality and other noise - induced decoherence effects. While the AER scheme has proven effective for two - party end - to - end entanglement, there is a growing need to support multipart ite entangleme nt among multiple remote endpoints. Such capability is essential for enabling applications li ke quantum - safe m ulti - party computation and conference key agreement, where a shared secret key must be established simultaneously among all participants. A practica l approach is to employ multipartite entang lements , f or example, Greenberger - Horne – Zeilinge r ( GHZ) states among the endpoints to realize secure multi - party key exchanges [11] . In this paper, we extend the DODAG - based AER framework and propose multipartite asynchronous entanglement routing ( MAER) to enable the distributed generation of m ultipartite entanglements across distant nodes. MAER is d esigned to oper ate in a full y distr ib uted and asynchronous manner, usi ng only local link - state information while maintaini ng scalabilit y across large qu antum networks. We also demonst rate MAE R’s per formanc e adva ntages over synchronous approaches. While Meignant et al. (2019) [6] construct multipartite ent angled states under idealized, globally informed synchronization, MAER achi eves superior performance without requiring global timing coor dination or centralized control. In optics - based repeaters, t he success probability for an ! - qubit fusi on operati on decreases exponentially, following a rate of "#$ ! [4] . This implies that minimizing the number of higher - order fusion gates is advantageous. Specifically, for GHZ states, the MAER protocol r equires only a s ingle n - fusion ope ration to establish an n - party state. This approach is tailored to GHZ - type entanglement and may not directly generalize to generating arbitrary multipartite states such as graph states or cluster s tates, which typically requi re more elaborate fusion or entangling procedures. We asse ss MAER' s perfo rmance t hrough s imulat ions across various network configurat ions. These simulations show consistent improvem ents in end - to - end entanglement rates across multiple topologies, such as grid, barbell, and random graphs. The advantage of the MAER scheme becomes particularly pronounced when quantum memories possess longer coherence times, as MAER can retain and utilize stored entanglement across multiple time slots without synchronization resets. Consequently, as memory technology advances a nd coherence times extend, the achievable entanglement rates under MAER continue to improve, further widening the pe rformance gap ov er synchronous schemes. Moreover, a tree - like instant topology, such as a DODAG, facilitates interconnection among multiple network layers via root nodes. These results suggest that the proposed protocols can play a key role in reali zing scalable quantum internetworking as quantum memory and repeater technologies mature. Recently, an AER - based extension , the DODAG - X protocol [7], was proposed to enhance multipartite entanglement distribution across multiple receivers. This approach inherits the asynchronous DODAG structure introduced in AER and focuses on optimizing the efficiency of entanglement dissemination within a fixed routing topology. In contrast, the proposed MAER generalizes this framework to su pport fully asynchronous multipartite routing, where both to pology forma tion and ent anglement gen eration proceed concurrently without global synchronization. The re st of t he pap er i s or ganized as follows. Section II introduces the fundamental conce pts that underpin MAER and multipart ite enta nglement r outing in quantum ne tworks. Section III presents the details of implementing the MAER protocol using DODAG. Section IV describes the simulation setup and evaluates the protocol’s performance under various configurations. Section V concludes the paper. II. P RELIMINARIES This section presents fundamental concepts that underpi n the study of routing for multipartite entanglement in quantum networks. A. Dir ect - link Entanglement As mentioned, quantum repe aters have been designe d to expand the reach of entanglement generati on. They use Bell - state measurement (BSM), i.e., entanglement swapping, to project two entangled pairs into a distant entangled state between nodes that are not directl y connected. BSMs have been successfully implemented in various physi cal systems and are commonly used in quantum networks to link shorter entanglement chains into longer - distance clusters [12] . Quantum capabilitie s at network nodes during the current noisy intermediate - scale quantum (NISQ) era benefit from these probabilistic BSMs, which accommodate losses in optical fibers and the li mitations of quantum hardware [1] . As quantum networks evol ve beyond two - party communication, the growing demand for multipartite entanglement has motivated the use of fusion measurements, which go beyond s wapping and enab le the creati on of GHZ states among multiple nod es. GHZ fusion measur ements build Published in the 2026 IEEE 16th Annual Computing and Communication Workshop and Conference (CCWC), Las Vegas, NV, USA, 2026 , pp. 053 3 - 0541, doi: 10.1109/CCWC67433.2026.11393739. on the concept of BSM by merging multiple entangled states into a single GHZ state, facilitating multipartite entanglement among nodes without direct links. This advancement necessitates new routing protocols f or multi - party rather than two - party routing s cenarios. Moreover, it is import ant to note tha t a cla ssical network is always assumed to underpin the q uantum network, handling routing computations and disseminating routing information. Essentially, each node in the quantum network communicates via a classical ne twork, aligning with the principles of local ope rati ons and clas sic al c omm uni cati ons (LO CC) . Th is se tup is typical in hybrid quantum - classical networks and is standard in quantum routing techniques. Once candidate paths are established via classical routin g, repeaters perform entanglement swapping or fus ion measurements alongside ongoing classical signaling. After each Bell - state measurement or fusion operat ion, t he meas urement outcomes are communicated through the classical network so that the end nodes ca n apply the appropriate Pauli corrections and complete the entanglement distribution. These message exchanges introduce classical latency proportional to network distance and hop count. In our simulation model, classical signalling delays a re not explicitly accounted for, as the focus is placed on quantum - layer timing and coherence effects. This simplification is consistent with prior st udies [4] [5] , whi ch assume that classical communication time is negligible compared with the timescale of entanglement generation and swapping. Nevertheless , in practical implementations, classical feedforward for Bell - state measurement outcomes and ro uting coordination would introduce additional latency, which may become significant in long - haul or high - speed networks. Incorporating these classical communication effects remains an important direction for future work. B. Chal lenges in Ent anglement Routi ng With re peater s enab ling e ntangl ement between remote nodes, t here is a need for routing protocols that efficiently identify paths to establish entangled connections among arbitrary nodes within a network. However, quantum networks in the NISQ era pres ent unique challenges that may not be found in classical networks, necessitating either adaptations or new designs tailored for quantum network environments: • Entanglement as A Communi cation Reso urce: Unlik e classical networks, where data packets are transmitted and relayed through intermediate nodes from t he source to the destination, quantum networks utilize end - to - end or remote multipartite entanglement estab lished via intermedia te nodes. Such entanglement serves as a communication resource for transferring qubits (via teleportation) or exchanging secret keys (through QKD). This approach enhances security, as data does not physical ly traverse the net work. Howe ver, this additional layer of entanglement distribution introduces unique challenges. For instance, while qubits can be tem porarily stored in quantum memories for synchronization, they cannot be amplified or regenerated like classical signals due to the no - cloning theorem, which prohibits duplicating unknown quantum states. • Hardware Imperfections: Quantum hardware in the NISQ era remains inherently noisy and unreliable, which si gnificantl y affect s core operations in quantum networks, including direct - link entanglement generation, entanglement swapping, and fusion measurements. These operations are probabilistic and subject to failure due to factors such as gate infidelity , photon loss, mode mismatch, and limited detector efficiency. Consequently, establishing and maintaining stable entanglement links is often inefficient and u nreliable. Routing protocols must be designed with these physical - layer imperfections in mind, often by m odeling success probabilities for each operation and incorporating error - tolerant mechanisms or redundant paths to increase reliability in practical im plementations. • Decoherence a nd Photon Los s: Quantum in formation is inherently time sensitive due to decoherence, which causes stored quantum states to lose coherence through interactions with their environment. In quantum networks, decoherence primarily affects stationar y qubits held in quantum memories. In contrast, photon loss occurs during transmission through optical fibers or free - space channels and represents a separate source of error. Consequently, networking pr otocols must ensure that entanglement generation, sto rage, and routing operations are completed within the available coherence time of t he memory element s, while als o accounting for transmission losses alon g optical links. • Ne twork I nformation P ropa gation : In a quantum network, routing decisions may depend on the comprehensive knowledge of the instant topology, meaning tha t every nod e must know t he status of all direct - link entanglement links before routing can commence. However, as the network scales, disse minating this i nformation across all nodes becomes increasingl y time - consuming. Due to the limited coherence time of entanglement links, some links may have already decohered by the time global link - state information is ful ly propagated. Therefore, there is a need for routin g schemes that do not rely on global knowledge of the current topology but instead use infor mation about adjacent links to perform pathfinding or routing in a distributed manner. • Network Scalability: As quantum networks expand to accommodate a growing number of users and increasingly co mplex applicatio ns, maintaining overall performance and reliability becomes more challenging. Larger networks demand more entanglement links, greater coordination among nodes, and more classical communication overhead to support entanglement routing and management. These scaling factors amplify the effects of decoherence, operation delays, and cumulative errors, especially under hardware constraints. Eff ective scalability requires routing protocols that efficiently manage en tanglement resour ces ac ross la rge topologies, minimize reliance on global knowledge, and dynamically adapt to changes in network size and structure while preserving the integrity of quantum information . Published in the 2026 IEEE 16th Annual Computing and Communication Workshop and Conference (CCWC), Las Vegas, NV, USA, 2026 , pp. 053 3 - 0541, doi: 10.1109/CCWC67433.2026.11393739. C. The Routing Problem and Existing Work As mentioned in Secti on I, i t is co mmon in quan tum network ent anglement routing schemes to structure time into discrete slots, each divided into two phases. With that, we can formulate the entanglement routing problem with a graph % & ' ( ) * that represents the physical structure of the quant um network. In this graph, each node +, - ' acts as a repeater, and each edge ., - ) indicates a physic al channel connecting two adjacent repeaters. The instant topology, % ′ / ' ′ ( ) ′ 0 derived from % & ' ( ) * , where ) ′ represents the direct - link entanglement links and ' ′ includes nodes interconnected by these links. Each edge . supports entanglement generation through a qubit pair between neighboring nodes. Each node possesses a limited number of qubits. For simplicity, only a single qubit on each side of a physical link is assumed, as shown in Fig. 1 . Due to operational uncertaintie s, entan glement g eneration on a direct link . has a success probability denoted as 1 & . * , which depend s on facto rs such a s physical distance and channel transmissivity, and photon loss. Similarly, the success probability of entanglement swapping at a repeater node, denot ed by 2 & + * , is primarily determined by the performance of the BSM apparatus. Key influences include detector efficiency, photon indist inguishability, memory retrieval fidelity, and channel loss. In practice, linear - optical BSMs are inher ently probab ilistic a nd can s ucceed with a probability up to 50% even under i deal conditions, with this probability further reduced by imperfections such as photon loss, finite coherence time, an d synchronization errors. For analytic al tract ability, and consistent with prior works on repeater - based entanglement routi ng [4] [5] [8] , we assume uniform probabilities 1 and 2 for entanglement generation and swapping across the network, respectively . This simplificat ion is reasonable fo r networks composed of homogeneous optimal links and repeater hardware. More heterogeneous configurations coul d instead assign 1 & . * and 2 & + * based on l ink - and node - specific physical pa rameters to capture variations in hardware performance and physical - layer conditions in future stu dies. Each entanglement is also assumed to h ave a constant coherence time, 3 "# , reflecting how long it can remain stable without significant degradation. Assuming a single connection request at a time, t he end - to - end entanglement rate, denoted by 4 , quantifies the number of remote entanglements formed per unit time T, which must not exceed 3 "# . The time for both phases of operation is counted as a single unit, set to 3 5 3 "# #6 , where m is an integer and 6, 7 " . For example, if 3 "# 5 6 , it suggests that the coherence time spans n unit times in that si mulation. As discussed earlier, fi nding a path wi th the globa l knowledge approach is well studi ed, but often impractical due to the extended time required to disseminate link - state information across the network. Most existing studies, Most existing studies , such as those by Shi and Qian (2020, Q - CAST) [5] , Meignant et al. (2019) [6] , and Negrin et al. (2024) [7] , adopt this paradigm, rely on such global knowledge, employing synchronization mechanisms to propagate the instant topology after the first phase. This allows straightforward path identification using shortest - path algorithms during the second phase. In contrast, relying on local knowledge of the instant topology is more feasible in practice, though it complicates pathfindi ng due t o limited information about the overall network topolo gy [8] . Nonetheless, once a path consisting of 8 edges and 8 9 " repeaters is successfully established after t he completion of several time slots, and a remote entanglement between the end nodes can be achieved with a probability of 2 $ %& ' ( . Fig. 2. DODAG - based entanglement routing and its update. III. M ULTIPARTITE A SYNCHRONOUS E NTANGLEMENT R OUTING This section i ntroduces MAER. A. Tree - based Asynchr onous Routing The MAER scheme builds upon the f ramework intr oduced in our prior work [8] [9] . In this scheme, nodes manage and update the instant topology in a distributed manner by exchanging DODAG messages over classical channels, allowing the instant t opology to evolve dynamically as a tree. Analyses involving a s panning tree i n this context a re also discussed in [8] . A DODAG in MAER is structur ed with all edge s directed towards a designated root node. The root node can be pre - assigned based on network role (e.g., a data center or service node) or dynamicall y elected based on network metrics such as degree centrality or memory availabilit y. In our simulations, the geometric center of the network topology i s designated as the root to minimize the average hop distance to all nodes. The DODAG cons truction rule en sures loop freedom . Each node selects only a paren t with a strictly lower rank value. Because ranks monotoni cally decrease toward t he root, cyclic dependenci es cannot occur. This mechanism is analogous to the classical Routing Protocol for Low - Power and Lossy Networks (RPL) , where ordered rank s prevent loops. The DODAG is con structed through the exch ange of control messages, and in the quantum setting, nodes use rank (a) Physical topology (b) Instant topology DAO DAO D AO DAO DIS DIS DIS DIO DIO DIO DIO DIS DIS DIO DIS DIO DIS DIO DIO DIS DIO DIO DIO DIO DIS DIS DIS DIS DIS DIS DIS DIS DIS DIS DIS DIS DIS DIS DIS DIS DIS DIS DIS DIS DIS DIS DAO DIO DIO DIO DIO DIS DIS DIO DAO DAO DIO GHZ Fusion Entanglement Swapping DIS DIS DIO DIO DIO DIO DIS DIS DIO DAO DIO (c) Swapping and GHZ fusion (d) End- to -end entanglements : DODAG root : DODAG member : Unattached node : Quantum-classical link : Direct-link entanglement : Bipartite/Multipartite end- to -end entanglement / A2 B2 A1 B1 C1 A2 B2 A1 B1 C1 A2 B2 A1 B1 C1 A2 B2 A1 B1 C1 Published in the 2026 IEEE 16th Annual Computing and Communication Workshop and Conference (CCWC), Las Vegas, NV, USA, 2026 , pp. 053 3 - 0541, doi: 10.1109/CCWC67433.2026.11393739. values to represent their logical distance from the root. These ranks facilitate the selection of optimal routes for entanglement distribution and simplify path management by enabling distributed routing decisions centered around the root node. Each node, including consumers, maintains only local knowledge of its neighboring links and parent rank values within the DODAG. Nodes neither require nor store global network topology information. Fig. 2 demonstrates the gr owth of a DODAG ins tance from a designated root node under the MAER protocol, whic h establishes end - to - end entanglement between end nodes, such as (A1, B1) and (A2, B2, C2) . Nodes already included in the DODAG ar e depicted in green, while nodes not included are shown in grey. Nodes within the DODAG can serve as parents to other nodes during to pology expansion. As shown in Fig. 2 (a) , u njoined ( gray) nodes initiat e the joining process by sending DIS (DODAG Information Solicitation) messages to their neighboring nodes . Upon receiving a DIO (DODAG Informatio n Object) message from a neighbor already in the DOD AG, the grey node replies with a DAO (Destination Advertisement Object) message to formally request inclusion. The neighbor then assigns a rank to the requesting node and integrates it int o the DODAG. Only nodes that are not yet part of the DODAG broadcast DIS messages. Once a nod e successful ly joins and obtains a rank, it stops transmitting DIS . Instead, it responds to new solicitations with DIO messages, allowing the tree to expand outward from the root. If no DIO messages are received, the unjoined node continues broadcasting D IS messages until a valid response is received or another neighboring node admits it. As the DODAG evolves ( Fig. 2 (b) - (d)) , routing p aths gradually form by selecting parent nodes with t he lowest rank. In the baseline MAER configuration, the DODAG expands outward from a designat ed root node, which gradually attracts join requests from consumers and intermediate nodes . Alternativel y, one coul d imagine a consumer - initiated inward expansion, in which each e nd no de independently attempts to connect to the root. In that case, multiple pa rtial tr ees would f orm concurr ently and mer ge when they encounter a c ommon ancestor . W hile this ap proach could reduce the initial setup latency for sparsely connected nodes, it introduces coordination overhead to resolve rank conflicts and maintain acyclicity during tree merging. The present MAER formulation avoids this complexity by all owing all joining nodes , including request nodes , to send solicitation (DIS) messages only toward existing DODAG members, ensurin g consistent rank orderi ng from the root outward. A furt her e xtension involves multi ple r oot n odes ( multi - root MAER), which could represent distinct service centers or access points. In this configuration, independent DODAGs would form around each root and could later be f used through inter - root entanglem ent or GHZ - fusion operations to link otherwise separate clusters. While multi - root designs may improve robustness and load balancing, they also complicate coordination and rank assignment across overlapping r egions. Investigating such multi - root synchroniz ation and i nter - tree fusion mechanisms is an interesting direction for future work. B. Topology Update for Multipartite St ates The root node does not require prior global knowledge of consumer locations. Instead, end nodes periodically broadcast local j oin (DIS) messages over classical channels, which are relaye d until receive d by a DODAG member. Through subsequent DIO and DAO exchanges, the root node gradually learns which nodes have joined and t heir relative ranks, enabling the formation of a dynamic tree without centralized location tracking. Classical comm unication for these control messages occurs asynchronously alongside enta nglement generation attempts. Consider Alice , Bob, and Charl ie, located at : ' , ; ' , and C1 , respectively, in Fig. 3 , wh o aim to establish a three - party GHZ state but lack direct opt ical link s connect ing them. As the DODAG expands from the root , these end nodes attempt to join the tree as described above. Each node continuously transmits DIS messages until successfully admitted into the DODAG, as ill ustrated i n Fig. 3( a) and (b). After joining the DODAG, ea ch of the three end nodes establishes an end - to - end entanglement with the root node through a sequence of entanglement - swapping operations, if required. Once these operations succeed, three distinct entanglement links are f ormed between the root node and the end nodes, as indicated in Fig. 3 (b) . The root node then performs a fusion measurement on it s t hree qubi ts. If the fusion succeeds, a remote GHZ state is generated among Alice, Bob, and Charlie , as shown in Fig. 3 (d). This GHZ state can then be utilized for various quantum applications, such as multi - party QKD or distributed computation. After the requesting end nodes consume a GHZ entanglement , the network updates accordingly to accommodate subsequent connection requests. Only the entanglement links involved in the established GHZ state are consumed, while unused direct - link entanglement remains available for later time slots or until lost due to decoherence. Notably, the propos ed s cheme supports both two - party and multipart ite enta nglement r equests an d require s only a si ngle n- fusion operation to establish an n - party GHZ state. C. Path Selection Path selection becomes rel atively flexible once the end nodes are integrated into the DODAG. Each node selects a parent wit h a lower rank to facilitate entanglement swapping toward the root n ode. If there is only one available pare nt, the node simply chooses it. When multiple parents are available, the node prefers the one with the lowest rank, as this corresponds to the shortest logical distance to the root. In cases where mul tiple parents shar e the same minimum rank, the node can arbit rarily choose among them , as we assume no difference in link qu ality or reliability. It might initially appear necessar y for every pair of end nodes to establish independent paths to the root, since only one direct - link entanglement can exist between any two nodes. Fig. 3 illustrates that this approach can be wasteful. For instance, < ) could, in principle, creat e an end - to - end link with the root through : ' , while : ) does so via node = . However, such routing would consume the direct - link entanglement between : ' and the root , which prevents the successful completion of the three - party request among : ' , < ' , and > ' , and would additionally deplete the root’s direct link to the node = . A more efficient alternative is t o allow l ocal aggregation , as shown in Fig. 3 (c). Node = is already the Published in the 2026 IEEE 16th Annual Computing and Communication Workshop and Conference (CCWC), Las Vegas, NV, USA, 2026 , pp. 053 3 - 0541, doi: 10.1109/CCWC67433.2026.11393739. parent of : ) and < ) . T hen, node : ) and < ) can establish their end - to - end entanglement directly through their common parent node = , without inde pendently c onnecting t o the root . This local - path strategy preserves valuable direct - link entanglement resources, enabling simultaneous f ulfillment of other requests such as the thr ee - party state ( : ' ( < ' ( > ' ). Fig. 3. DODAG - based bipartite and mult ipart ite entangl ement routing. Fig. 4 illustrates two distinct approaches for generating three - party GHZ states. The f irst adopts the convent ional method, in whic h a common pa rent p erforms a GHZ - fusion measurement to ent angle ( : ' ( < ' ( > ' ) , as shown in Fig. 4 (c) . The second employs a Hadamard - plus - CNOT fan - out principle [13] to generate the GHZ state ( : ) ( < ) ( > ) ) without centralized fusion. As shown i n Fig. 4 (c), the root node first performs an entangl ement - swapping operation to connect the Bell pai rs &: ) (? @AAB * and ( @AAB( ?< ) * , thereby creating an end - to - end Bell pair between : ) ? and < ) . The pa rent node : ) then applies a Hadamard gate to its qubit entangled with > ) , generating the superposition &CDE F ? C"E*#G$ . Next, : ) performs a CNOT operation usi ng thi s qubit as the control and its qubit entangled with < ) as the target. This sequence locally extends the two Bell pairs into a three - party GHZ stat e , including : ) , ; ) , and > ) w ithout requiring additional swapping. In our MAER scheme, both centralized and distributed strategies are employed for multipartite entanglement generation, depending on network conditi ons and resource availability. When multiple nodes share a common parent, the parent can act as a local fusion center , performing the necessary entanglement - swapping or Hadamard - plus - CNOT fan - out operations to create GHZ states without i nvolving the root. Alternatively, when the participating nodes are located in different DODAG branches, the root node performs G HZ fusion to establish the multipartite entanglement across distant clusters. IV. E VALUATION This section assesses the proposed scheme by detailing the simulation settings and presenting the results. To contextualize the evaluation, recall that in synchronous routing schemes, such as [5] and [6] , all nodes operate in globally synchr onized time slots . In contrast, the proposed MAER e xecutes entang lement generat ion and s wapping independently acro ss nodes without global timing coordination . Fig. 4. Two approaches for gene rating th ree - party GHZ states . A. Simulat ion Setting In the simulation, we assume fixed success probabilities for direct - link entanglement generation and repeater operations. Speci fically, each direct link succeeds with probability 1 , and each repeater operation (e.g., entanglement swapping, GHZ fusion, or Hadama rd - plus - CNOT gate) s ucceeds with probability 2 . To al ign with prior synchronous approaches for comparison, we define a unit of time as a time slot. The coher ence time 3 *+ (often denoted 3 ) ) represents the duration over which stored entanglement remains stabl e [14] . We furth er assum e that attempts to establish direct - link entanglement and to operate a repeater are independent. Once a path of le ngth 8 is established within the instant topology, the probability of successfully generating a GHZ state along that path is given by 4 5 2 $ %& ' ( . Because an entanglement attempt is performed per unit ti me, this success probability directly corresponds to the expected end - to - end entanglement rate per unit time. We eva luate MAER with three consumer s (e nd n odes) per experiment. Unless noted ot herwise, we use the graph - theoretic shortest - path hop di stance rather than the Euclidean lay out distan ce. For a consumer triple HI( + ( J K , (a) Initial Rank As signment (c) Resource Aggregation Rank = 0 Rank = 1 Rank = 0 Rank = 0 Rank = 2 Rank = 1 GHZ Fusion Swapping Rank = 0 Rank = 2 Rank = 1 : DODAG root : DODAG member : Unattached node : Bipartite/Multipartite end- to -end entanglement / : DAO message : DIO message (a) Hierarchical T opology Formation (d) End- to -end entanglements A1 B1 C1 A2 B2 A1 B1 C1 A2 B2 A1 B1 C1 A2 B2 A1 B1 C1 A2 B2 (a) Initial Rank A ssignment (c) Resource Aggregation Rank = 0 Rank = 1 Rank = 0 Rank = 0 Rank = 2 Rank = 1 GHZ Fusion Swapping Rank = 0 Rank = 2 Rank = 1 : DODAG root : DODAG member : Unattached node : DAO message : DIO message (a) Hierarchical T opology Formation (d) End- to -end entanglements A1 B1 C1 A2 B2 C2 C2 B2 C2 A2 A2 A2 A2 A1 B1 C1 B2 A1 B1 C1 A1 B1 C1 B2 : Bipartite/Multipartite end- to -end entanglement / Hadamard + CNOT Gate Published in the 2026 IEEE 16th Annual Computing and Communication Workshop and Conference (CCWC), Las Vegas, NV, USA, 2026 , pp. 053 3 - 0541, doi: 10.1109/CCWC67433.2026.11393739. we de fine the triplet distanc e L 5 ' , M N & I( + * F N & +( J * F N & J( I * O , where N & P(P * is the shortest - path hop count on the physical topology. When plott ing p erform ance v ersus distance Q , we target a desired value Q - and sampl ing consumer tripl es unifor mly at random under the constraint Q - R Q - 9 S( T Q - F S U , with tolerance S 5 ?"? hop (unless otherwise specified). For each parameter combination and topology, we draw . V 5 "DD independent consumer triples and reports the mean end - to - end entanglement. Since c entrally located nodes benefit from higher path di versity (larger network min - cut) than peripheral ones , we randomly sample at a fixed Q - averages over these effects and prevents bias toward particularly favorab le geometries. Each simulation runs for 20,000 iterations to compute the average multipartite entanglement rate. Different physical topologies are generated by NextworkX [15], including a grid network, a barbell net work with a single backbone li nk, and a random graph in which each node has an average of 4 links, each consisting of 100 network nodes . At the begin ning of each simulation, the central node of the physical topology is designated as the root, and a t hree - user request is then initiated by randomly selecting n ode s located at the spec ified graph distance. Each sel ected node attempts t o join the DODAG by e stablishin g a direct link with existing members. As successful links form, the DODAG dynamically expands, and rank values are assigned to newly joined nodes based on their distance from the root. As the DODAG evolves, it att empts to form a connected structure t hat i ncludes all three end users. If no such connection is established within a unit of time, the GHZ entanglement generation rate for that period is recorded as zero. Suppose at least one valid path is identified. I n that case, the shortest path, potentially through a common parent node rather than the root, is selected and use d to compute the corresponding success probability for multipartite entanglement generation. In our simulations, we abstract away entanglement fidelity, assuming that all successful direct - link entanglement attempts yield usable pairs of uniform quality. While fidelity maintenanc e is crucial for p ractical implementati ons, it is beyond the scope of this study and is left for future study. B. Resu lts Unless otherwise speci fied in t he ca ption, Fig. 5 (a) - (b), and Fig. 6 (a) use the grid topology (10×10, 100 nodes) and consumer triples sampled by the procedure above with S 5 " and V 5 "DD trials per point. As shown in Fig. 5 , the performance of traditional synchronous protocols [5] [6] is labelled as "Syn" in the charts. The result shows that the proposed MAER prot ocol based on DODAG achieves higher end - to - end entanglement rates for remote three - qubit GHZ generation than synchronous methods, particularly when the coherence time exceeds 1 . The purple - dashed lines, which emerge as the coherence time appr oaches infinity, represent the estimated upper bounds on the entanglement rates achievable by MA ER under the simulation setti ngs. The end - to - end entanglement rate achieved by MAER increases steadily with longer coherence times. This suggests that as quantum technology advances, enabl ing quantum memory to maintain entangled states for extended periods, the advantage of asynchronous routing will continue to grow relative to synchronous schemes . Fig. 5. Rate vs. graph di stance with var ying coher ence ti mes. To fur ther evaluate performance under d ifferent parameter settings, we tested various combinations of the direct - link success probability 1 and the repeater operation success probability 2 . Excep t for cases w here the coheren ce time equals one and 1 is small, MAER consistently outperforms synchronous methods across all tested combinations, as shown in Fig. 6 (a). It also demonstrates that MAER achieves a consistently higher upper bound for multipartite end - to - end entanglement rates than synchronous protocols under the same conditions. Moreover, as shown in Fig. 6 (b), the proposed MAER protocol maintains its advantage in achieving higher multipartite end - to - end entanglement rates across all t ested network topologies , including a grid, a barbell, and a random graph. Each network topology used in the simulation contains 100 nodes. The grid topology is a ten - by - ten square lattice, where each interior node is connected to four neighbors. The barbell topology consists of two fully connected clusters (cliques), each with 50 nodes, connected by a single backbone link betwe en one node in each cluster. The random graph topology is generated using the Er dős – Rényi model with 100 nodes and a connect ion p robability of Published in the 2026 IEEE 16th Annual Computing and Communication Workshop and Conference (CCWC), Las Vegas, NV, USA, 2026 , pp. 053 3 - 0541, doi: 10.1109/CCWC67433.2026.11393739. 0.04. Results for the grid and random graph are similar, likely due to their comparable average degree of approximately four under the given configuration, despite differences in their structural properties. Considering a generalized sc enario wit h an a rbitrary number n of end nodes forming an ! - qubit GHZ state, we conducted additional simulations to evaluate MA ER's performance u nder varying numbers of participants . Specifically, we exa mined cases where the number of end nodes ! ranged from 3 to 7, as shown in Fig. 7 . To maintain comparable spatial separation between nodes as ! increases, the average pairwise graph distance Q among end nodes was set proportionally to ! , defined as Q 5 ?W? X ! . This proportional scaling prevents newly added part icipants from clustering near existing participants and ensures that network load and path diversity scale roughly linear ly with the multipart ite group si ze. If Q were held constant whi le increasing ! , additional users would be placed within a fixed spatial region, leading to overlapping paths, shared repeaters, and artificial correlation between entanglement - generation attempts. While such a setting might be interesti ng for analysing local congest ion e ffects, our goal here is to study MAER’s scalabili ty with system size under c omparabl e topological spreading. Across all these simulations, the MAER protocol consistentl y achieved higher e nd - to - end entanglement rates for ! - qubit GHZ states compared with existing synchronous approaches, for both grid ( Fig. 7 (a )) and random ( Fig. 7 (b)) topologies. Fig. 6. Rate vs. p across various coherence times and Rate vs. d across various topologies . Based on the simul ation result s and subsequent a nalyses, we substanti ate the advant ages of employ ing the MAER protocol with a DODAG str ucture for multipartite entanglement distribution. These advantages are evident across sever al key dimensions: (1) The end - to - end entanglement rate for remote GHZ states under MAER shows a positive correlation with increased coherence times, indicating improved performance as qua ntum memories become more s table; (2) MAER is adaptable to diverse network topologies — includ ing g rid, barbell, and random graphs — while consistent ly outperfor ming synchron ous methods; (3) In simulat ions involvin g dynamic ! - party GHZ generation, MAER maintai ns high end - to - end entanglement rates even as the number of end nodes increases, demonstrating its effectiveness in handling multi partite entanglement requests of varying sizes; (4) These proper ties collectively underscore MAER’s strong scalability, making it well - suited for future quantum networks expected to support larger user bases and mo re compl ex quantum applications . Fig. 7. Rate vs. the number of nodes and across v arious topologies. V. C ONCLUSION This s tudy ad vances quantum ne twork co mmunications by ext ending asynchronous, tree - based routing schemes to support both two - party end - to - end entanglement and more complex multipartite entanglement, such as GHZ states. The proposed MAER protocol leverages only local knowledge of entanglement links, eliminates the need for synchronized operations, and conserves unused entanglement resources. Simulation results demonstrate t hat MAER significantly outperforms existi ng synchronous methods, particularly as coherence ti me increases. These findings highlight the adaptability and effectiveness of asynchronous routing in supporting multipartite entang lement across diverse network topologies. 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