Abstract Multipartite entangled states, such as Greenberger–Horne–Zeilinger (GHZ) states, are important resources in multiparty quantum networking tasks. We consider protocols for generating such states from networks of Bell pairs and local operations and classical communication. We present a computationally-efficient protocol for generating GHZ states that is also efficient with respect to the number of consumed Bell pairs, (local) gates, and Bell-pair sources. Our protocol: (1) requires O ( N ) gates in a network with N nodes, independent of the network topology; (2) has time complexity O ( N 2 ), avoiding the Steiner tree and any other computationally-hard problem; (3) maintains a near-optimal number of consumed Bell pairs. Numerically, our protocol outperforms those based on (approximate) Steiner trees with respect to the number of gates and Bell-pair sources. We prove that the minimal Bell-pair source cost is given by solving the graph-theoretic dominating set problem, and we demonstrate numerically that our protocol is nearly optimal for this quantity. Finally, we analytically characterize the impact of noisy Bell pairs and gates on the fidelity of the distributed GHZ states.
Abstract Multipartite entangled states, such as Greenberger–Horne–Zeilinger (GHZ) states, are important resources in multiparty quantum networking tasks. We consider protocols for generating such states from networks of Bell pairs and local operations and classical communication. We present a computationally-efficient protocol for generating GHZ states that is also efficient with respect to the number of consumed Bell pairs, (local) gates, and Bell-pair sources. Our protocol: (1) requires O ( N ) gates in a network with N nodes, independent of the network topology; (2) has time complexity O ( N 2 ), avoiding the Steiner tree and any other computationally-hard problem; (3) maintains a near-optimal number of consumed Bell pairs. Numerically, our protocol outperforms those based on (approximate) Steiner trees with respect to the number of gates and Bell-pair sources. We prove that the minimal Bell-pair source cost is given by solving the graph-theoretic dominating set problem, and we demonstrate numerically that our protocol is nearly optimal for this quantity. Finally, we analytically characterize the impact of noisy Bell pairs and gates on the fidelity of the distributed GHZ states.
The distribution of high-quality Greenberger-Horne-Zeilinger (GHZ) states is at the heart of many quantum communication tasks, ranging from extending the baseline of telescopes to secret sharing. They also play an important role in error-correction architectures for distributed quantum computation, where Bell pairs can be leveraged to create an entangled network of quantum computers. We investigate the creation and distillation of GHZ states out of nonperfect Bell pairs over quantum networks. In particular, we introduce a heuristic dynamic programming algorithm to optimize over a large class of protocols that create and purify GHZ states. All protocols considered use a common framework based on measurements of nonlocal stabilizer operators of the target state (i.e., the GHZ state), where each nonlocal measurement consumes another (nonperfect) entangled state as a resource. The new protocols outperform previous proposals for scenarios without decoherence and local gate noise. Furthermore, the algorithms can be applied for finding protocols for any number of parties and any number of entangled pairs involved.
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.
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.
In quantum networks, multipartite entangled states distributed over the network are useful in implementing and supporting many quantum network applications for communications, sensing, and computing. The focus of our work is to de-velop techniques to efficiently generate distributed Greenberger-Horne-Zeilinger (GHZ) states, a special class of multipartite entanglement states. Prior works on generating GHZ states have focused on the objective of minimizing the number of maximally entangled (bipartite) pairs (EPs), while ignoring the stochastic nature of quantum processes and assuming uniform network links for generating EPs. In contrast, in our work, we take into consideration the stochastic nature of quantum networks, and focus on maximizing the expected generated rate of the GHZ states under given fidelity constraints. In this context, we develop two efficient generation schemes, viz., Fusion - Retain - only and General Fusion, comprised of optimal or near-optimal sub-steps. Both schemes, at a high-level, first determine a way to “connect” the nodes over which the GHZ state is to distributed, and then, determine a sequence of fusion operations on the EPs created over the connections. Using extensive simulations over a quantum network simulator (NetSquid), we demonstrate the effectiveness of our developed techniques and show that our schemes outperform prior work as well as a simple centralized approach by up to orders of magnitude while generating GHZ states of tolerable fidelity.
Distributing multipartite entanglement is a prerequisite for scalable quantum networks. Networks restricted to local operations and shared randomness (LOSR) avoid the quantum-memory and latency costs associated with the real-time classical communication required by LOCC-based networks. However, when only bipartite sources are available, LOSR networks cannot prepare useful GHZ states. In earlier work, we conjectured that multipartite sources overcome this limitation and supported this claim with a single numerical example. In this work, we prove the conjecture for regular and uniform networks of arbitrary size. By identifying the hyperedges of the network with the coordinates of a linear code, we show that whenever the edges incident to each node form an information set, a fixed collection of local unitaries, namely the local decoders of the code, transforms the source state into an (N)-party GHZ state with fidelity (d^{m-M}), without requiring any classical communication. Here, (m) denotes the number of edges incident to each node and (M) the total number of edges in the network. For the complete ((N-1))-uniform hypergraph (K_N^{(N-1)}), this fidelity reduces to (1/d). We further prove that this value is optimal among all local-unitary strategies and exceeds the best fidelity achievable using only bipartite sources. For example, in the four-node case, the optimal fidelity is (1/2), compared with the bipartite bound of (1/8). These results demonstrate that multipartite sources, together with shared randomness, can replace real-time classical communication for entanglement distribution.
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.