The effective routing of entanglement over a quantum network is a fundamental problem in quantum communication. The distribution and reshaping of multipartite entanglement over a quantum network requires scalable protocols that adapt to the underlying topology. Graph states provide a convenient framework for this challenging task, as they encode global entanglement in a structured way that can be locally manipulated to produce a variety of target states, without requiring additional long-distance quantum operations. In this article, we propose graph-state-based routing protocols for sharing GHZ states, achieving larger sizes than those achieved in the existing works for given network topologies. For this improvement, we consider tree structures connecting the users participating in the final GHZ states, as opposed to the linear configurations used in the earlier works. In particular, for grid networks, we show special constructions of such trees that achieve larger GHZ states than the prior works. Moreover, if the user nodes along which the entanglement is to be routed are pre-specified, a strategy is proposed to accomplish this routing.
The effective routing of entanglement over a quantum network is a fundamental problem in quantum communication. The distribution and reshaping of multipartite entanglement over a quantum network requires scalable protocols that adapt to the underlying topology. Graph states provide a convenient framework for this challenging task, as they encode global entanglement in a structured way that can be locally manipulated to produce a variety of target states, without requiring additional long-distance quantum operations. In this article, we propose graph-state-based routing protocols for sharing GHZ states, achieving larger sizes than those achieved in the existing works for given network topologies. For this improvement, we consider tree structures connecting the users participating in the final GHZ states, as opposed to the linear configurations used in the earlier works. In particular, for grid networks, we show special constructions of such trees that achieve larger GHZ states than the prior works. Moreover, if the user nodes along which the entanglement is to be routed are pre-specified, a strategy is proposed to accomplish this routing.
In quantum networks, one way to communicate is to distribute entanglements through swapping at intermediate nodes. Most existing work primarily aims to create efficient two-party end-to-end entanglement over long distances. However, some scenarios also require 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 solely on local knowledge of entanglement links, conserving unused entanglement and avoiding synchronous operations. This article extends this approach to multipartite entanglements, particularly the three-party Greenberger-Horne-Zeilinger (GHZ) states. It shows that our asynchronous protocol outperforms traditional synchronous methods in entanglement rates, especially as coherence times increase. This approach can also be extended to four-party and larger multipartite GHZ states, highlighting the effectiveness and adaptability of asynchronous routing for multipartite scenarios across various network topologies.
Distributing entanglement among multiple users is a fundamental problem in quantum networks, requiring an efficient solution. In this work, a protocol is proposed for extracting maximally entangled ($|{\text{GHZ}}_{n}\ensuremath{\rangle}$) states for any number of parties in a quantum network. It is based on the graph-state formalism and requires minimal assumptions on the network state. The protocol only requires local measurements at the network nodes and just a single-qubit memory per user. Existing protocols on bipartite entanglement routing are also improved for specific nearest-neighbor network architectures. To this end, the concept of majorization is utilized to establish a hierarchy among different paths in a network based on their efficacy. This approach utilizes the symmetry of the underlying graph state to obtain better-performing algorithms.
Building large-scale quantum computers, essential to demonstrating quantum advantage, is a key challenge. Quantum networks can help address this challenge by enabling the construction of large, robust, and more capable quantum computing platforms by connecting smaller quantum computers. Moreover, unlike classical systems, quantum networks can enable fully secured long-distance communication. Thus, quantum networks lie at the heart of the success of future quantum information technologies. In quantum networks, multipartite entangled states distributed over the network help implement and support many quantum network applications for communications, sensing, and computing. Our work focuses on developing optimal techniques to generate and distribute multipartite entanglement states efficiently. Prior works on generating general multipartite entanglement states have focused on the objective of minimizing the number of maximally entangled pairs while ignoring the heterogeneity of the network nodes and links as well as the stochastic nature of underlying processes. In this work, we develop a hypergraph-based linear programming framework that delivers optimal (under certain assumptions) generation schemes for general multipartite entanglement represented by graph states, under the network resources, decoherence, and fidelity constraints, while considering the stochasticity of the underlying processes. We illustrate our technique by developing generation schemes for the special cases of path and tree graph states and discuss optimized generation schemes for more general classes of graph states. Using extensive simulations over a quantum network simulator, we demonstrate the effectiveness of our developed techniques and show that they outperform prior known schemes by up to orders of magnitude.
Quantum networks will rely on entanglement distribution to enable multi-user applications such as distributed quantum computing and cryptography. While multipartite entanglement distribution routing protocols have been extensively studied on idealised grid topologies, less is understood about how real network structure shapes their performance and resource requirements. We present a systematic study of four routing protocols for multipartite entanglement distribution, each characterised by the number of paths (single-path and multi-path) and routing strategy (star-based and tree-based), over 81 real network topologies. We identified four distinct topology-dependent performance regimes, where: (i) all protocols perform poorly, (ii) tree-based protocols dominate, (iii) multi-path protocols dominate, or (iv) all protocols perform well. By correlating clusters with graph metrics, we also provide structural explanations for the varied performance of specific protocols. Additionally, motivated by the anticipated high cost of repeaters, we investigated the impact of repeater trimming on the performance of multi-path protocols. Topology strongly governs how far repeater nodes can be removed from the network while maintaining a given performance (distribution rate). For instance, in networks where only 80% of nodes operate as repeaters, well-performing topologies are able to retain over 90% of the distribution rate; whereas sparse, weakly connected graphs exhibit rapid performance degradation, retaining less than half of the distribution rate. Our results provide a topology-aware framework for protocol selection and infrastructure optimisation in future quantum networks, bridging routing design with cost-aware deployment strategies.
In entanglement distribution networks, communication between two nodes necessitates the generation of end-to-end entanglement by entanglement swapping at intermediate nodes. Efficiently creating end-to-end entanglements over long distances is a key objective. In our prior study on asynchronous routing, we enhanced these entanglement rates by leveraging solely the local knowledge of the node's entanglement links. This was achieved by creating a tree structure, particularly a destination-oriented directed acyclic graph (DODAG) or a spanning tree, eliminating synchronous operations and conserving unused entanglement links. In this article, we present a multi-tree approach with multiple DODAGs designed to improve end-to-end entanglement rates in large-scale networks, specifically catering to a range of network topologies, including grids and barbells, as well as realistic topologies found in research testbeds like ESnet and Internet2. Our simulations show a marked improvement in end-to-end entanglement rates for specific topologies compared to the single-tree method. This study underscores the promise of asynchronous routing schemes in quantum networks, highlighting the effectiveness of asynchronous routing across different network topologies and proposing a superior routing tactic.
Multipartite entangled states are great resources for quantum networks. In this work, we study the distribution, or routing, of entangled states over fixed, but arbitrary, physical networks. Our simplified model represents each use of a quantum channel as the sharing of a Bell pair; local operations and classical communications are considered to be free. We introduce two protocols to distribute, respectively, Greenberger-Horne-Zeilinger (GHZ) states and arbitrary graph states over arbitrary quantum networks. The GHZ states' distribution protocol takes a single step and is optimal in terms of the number of Bell pairs used; the graph states' distribution protocol uses, at most, twice as many Bell pairs and steps as the optimal routing protocol for the worst-case scenario.