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arXiv:2505.11632

Comparing GHZ-Based Strategies for Multipartite Entanglement Distribution in 2D Repeater Networks

Mohadeseh Azari, Amy Babay, Krishnamurthy, Prashant, Kaushik Parasuram Seshadreesan

Published May 16, 2025• 0 citations
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Abstract

We conduct a comparative study to determine the initial quality necessary to extend the distance range of an $N$-qubit GHZ state (the parent state) using two-dimensional repeaters. We analyzed two strategies for distributing initial GHZ states using a centralized quantum switch to determine if any of the strategies show benefits: i) A strategy that employs quantum memories at the switch to retain quantum states entangled with each client node, where memory usage at the switch scales linearly with the number of clients, and ii) A strategy predicated on GHZ measurements at the switch node without reliance on memory assistance. In the former scenario, the switches generate GHZ states and teleport them to the clients by utilizing remote Bell pairs that are asynchronously generated and stored in memory. Conversely, in the latter scenario, the switches perform GHZ projective measurements on freshly generated remote Bell pairs without requiring local storage at the switch. To enhance the distance range of GHZ-type entanglement distribution, we analyze the two approaches as foundational elements for a self-repeating, two-dimensional quantum repeater architecture. Here, the clients of the switch nodes become the 2D repeater nodes that store elementary GHZ states in quantum memories, that can then be fused together to generate long-distance GHZ-type entanglement between end users of the network. By examining the two strategies' entanglement distribution rates and fidelities, we identify the conditions under which the 2D repeater architecture enhances overall performance, and we determine whether either method is a superior building block for such a repeater structure. Our findings illuminate the identification of effective modalities for the long-distance multipartite entanglement distribution within quantum networks.

DOI
10.48550/arxiv.2505.11632

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We conduct a comparative study to determine the initial quality necessary to extend the distance range of an NNN-qubit GHZ state (the parent state) using two-dimensional repeaters. We analyzed two strategies for distributing initial GHZ states using a centralized quantum switch to determine if any of the strategies show benefits: i) A strategy that employs quantum memories at the switch to retain quantum states entangled with each client node, where memory usage at the switch scales linearly with the number of clients, and ii) A strategy predicated on GHZ measurements at the switch node without reliance on memory assistance. In the former scenario, the switches generate GHZ states and teleport them to the clients by utilizing remote Bell pairs that are asynchronously generated and stored in memory. Conversely, in the latter scenario, the switches perform GHZ projective measurements on freshly generated remote Bell pairs without requiring local storage at the switch. To enhance the distance range of GHZ-type entanglement distribution, we analyze the two approaches as foundational elements for a self-repeating, two-dimensional quantum repeater architecture. Here, the clients of the switch nodes become the 2D repeater nodes that store elementary GHZ states in quantum memories, that can then be fused together to generate long-distance GHZ-type entanglement between end users of the network. By examining the two strategies' entanglement distribution rates and fidelities, we identify the conditions under which the 2D repeater architecture enhances overall performance, and we determine whether either method is a superior building block for such a repeater structure. Our findings illuminate the identification of effective modalities for the long-distance multipartite entanglement distribution within quantum networks.
We introduce a repeater scheme to efficiently distribute multipartite entangled states in a quantum network with optimal scaling. The scheme allows to generate graph states such as 2D and 3D cluster states of growing size or GHZ states over arbitrary distances, with a constant overhead per node/channel that is independent of the distance. The approach is genuine multipartite, and is based on the measurement-based implementation of multipartite hashing, an entanglement purification protocol that operates on a large ensemble together with local merging/connection of elementary building blocks. We analyze the performance of the scheme in a setting where local or global storage is limited, and compare it to bipartite and hybrid approaches that are based on the distribution of entangled pairs. We find that the multipartite approach offers a storage advantage, which results in higher efficiency and better performance in certain parameter regimes. We generalize our approach to arbitrary network topologies and different target graph states.
The distribution of quantum entanglement between remote clients offers opportunities for secure communication, distributed quantum computation, and quantum-enhanced sensing. A key technology for allowing such a quantum network to extend over large distances is the quantum repeater, which typically employs a long-lived quantum memory with an optical interface. The past decade has seen tremendous progress in experimentally realizing the fundamental building blocks of these repeaters, but open questions remain on what architectures achieve optimal entanglement flows in multi-user quantum networks. Here, we propose a quantum router architecture comprising many quantum repeater nodes in a flexible photonic switchboard architecture to broker entanglement flows across such networks. We compute the rate and fidelity of entanglement distribution using this architecture using an event-based simulation platform. We find that the router's photonic switchboard improves the entanglement fidelity with the number of qubits per node, without a significant drop in the entanglement distribution rate. The proposed quantum router architecture uses present-day photonic switch technology such as photonic integrated circuits, opening a path to near-term deployable multi-user quantum networks.
Quantum networks will enable long-distance entanglement distribution through repeater nodes capable of both generating external Bell pairs with their neighbors—independently and identically distributed (i.i.d.) with probability p—and performing internal Bell State Measurements (BSMs), which succeed with probability q. These probabilities depend on the specific experimental parameters of the network. While global link state knowledge can maximize entanglement generation rates between any two consumers, it is often impractical due to the network's dynamic nature. This work evaluates a multipath routing protocol based on local link state knowledge, designed for time-multiplexed repeaters that can perform BSMs across different time steps. We employ simulations across various network topologies to characterize how consumer placement and network topology influence the utility of dynamic and static routing strategies. Results show that increasing the time multiplexing block length, k, enhances the average entanglement generation rate, though at the cost of higher initial latency. When a step-function memory decoherence model is introduced—where qubits are stored in quantum memory for a time that follows an exponential distribution—an optimal k emerges. As p decreases or the average memory lifetime increases, this optimal k grows, reflecting a trade-off where the advantages of time multiplexing must be balanced against the heightened risk of losing previously established entangled pairs.
We study entanglement generation in a quantum network where repeater nodes can perform nnn-qubit Greenberger-Horne-Zeilinger(GHZ) swaps, i.e., projective measurements, to fuse nnn imperfect-Fidelity entangled-state fragments. We show that the distance-independent entanglement distribution rate found previously for this protocol, assuming perfectly-entangled states at the link level, does not survive. This is true also in two modified protocols we study: one that incorporates l→1l \to 1l→1 link-level distillation and another that spatially constrains the repeater nodes involved in the swaps. We obtain analytical formulas for a GHZ swap of multiple Werner states, which might be of independent interest. Whether the distance-independent entanglement rate might re-emerge with a spatio-temporally-optimized scheduling of GHZ swaps and multi-site block-distillation codes remains open.
Quantum networks promise unconditionally secure communication and distributed quantum computing. Realizing these capabilities requires the reliable creation and maintenance of multipartite entanglement across large-scale networks. However, distributing complex entangled states among many nodes becomes increasingly challenging due to physical imperfections, architectural constraints, and the growing demands on network resources. This thesis presents practical methods that address two key facets of this broader problem. First, we introduce graph-theoretic protocols that generate GHZ states in Bell-pair networks using only local operations and classical communication, bypassing NP-hard subroutines while minimizing gate counts and Bell-pair consumption. Benchmarked on random network topologies and validated on IBM quantum hardware, these methods provide a scalable path to distributed quantum computing and multiparty communication. Second, we improve the performance of second-generation quantum repeater networks by incorporating bosonic quantum error correction. We show that memories with shorter coherence times, when protected by error correction, can outperform unencoded memories with significantly longer coherence times. We further address the problem of optimal memory-buffer allocation across repeater networks, introducing policies that reduce waiting times, thereby improving entanglement distribution efficiency. Overall, these results demonstrate practical and effective methods for improving performance and advancing the realization of near-term quantum networks.
We study the performance (rate and fidelity) of distributing multipartite entangled states in a quantum network through the use of a central node. Specifically, we consider the scenario where the multipartite entangled state is first prepared locally at a central node and then transmitted to the end nodes of the network through quantum teleportation. As our first result, we present leading-order analytical expressions and lower bounds for both the rate and fidelity at which a specific class of multipartite entangled states, namely, Greenberger-Horne-Zeilinger (GHZ) states, are distributed. Our analytical expressions for the fidelity accurately account for time-dependent depolarizing noise encountered by individual quantum bits while stored in quantum memory, as verified using Monte Carlo simulations. As our second result, we compare the performance to the case where the central node is an entanglement switch and the GHZ state is created by the end nodes in a distributed fashion. Apart from these two results, we outline how the teleportation-based scheme could be physically implemented using trapped ions or nitrogen-vacancy centers in diamond.