The distribution of multipartite entanglement is a key requirement for scalable quantum networks. While LOCC networks are theoretically universal, their reliance on quantum memories limits practical deployment. LOSR networks, which avoid real-time classical communication, offer a more feasible alternative but are fundamentally constrained when limited to bipartite sources. We conjecture that these limitations can be overcome with higher-dimensional entangled resources. Focusing on a square LOSR network with tripartite sources, we demonstrate a fidelity of$1 / 2$with GHZ states, surpassing the bound established in the literature. This result provides a concrete example of quantum advantage in LOSR networks and opens new directions for entanglement distribution under realistic constraints.
The distribution of multipartite entanglement is a key requirement for scalable quantum networks. While LOCC networks are theoretically universal, their reliance on quantum memories limits practical deployment. LOSR networks, which avoid real-time classical communication, offer a more feasible alternative but are fundamentally constrained when limited to bipartite sources. We conjecture that these limitations can be overcome with higher-dimensional entangled resources. Focusing on a square LOSR network with tripartite sources, we demonstrate a fidelity of1/2with GHZ states, surpassing the bound established in the literature. This result provides a concrete example of quantum advantage in LOSR networks and opens new directions for entanglement distribution under realistic constraints.
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.
The development of large-scale quantum communication networks necessitates the efficient distribution of quantum states to enable advanced cryptographic applications and distributed tasks. Multipartite entanglement is a key resource in many of these proposals, yet its generation is experimentally challenging, especially in noisy and lossy networks. While a substantial body of work focuses on the distribution of multi-partite entanglement in star-like topologies, practical implementations often rely on linear network structures constrained by existing infrastructure. In this work, we investigate the generation of high-fidelity multipartite entangled states in a realistic quantum network, leveraging the existing infrastructure of the Q-net-Q project-a real-world long-distance link connecting Berlin and Frankfurt via seven trusted relay nodes. Given that only bipartite entanglement sources are available in our setting and that the network is highly lossy, we explore the role of quantum memories in enhancing multi-partite entanglement distribution and identify key performance requirements. Furthermore, we analyze the feasibility and performance of cryptographic primitives-including (Anonymous) Conference Key Agreement and Quantum Secret Sharing-highlighting the scenarios where the use of multipartite entanglement yields clear advantages.
Quantum networks connect systems at separate locations via quantum links, enabling a wide range of quantum information tasks between distant parties. Large-scale networks have the potential to enable global secure communication, distributed quantum computation, enhanced clock synchronization, and high-precision multiparameter metrology. For the optimal development of these technologies, however, it is essential to identify the necessary resources and sub-routines that will lead to the quantum advantage, but this is demanding even for the simplest protocols in quantum information processing. Here we show that quantum networks relying on the long-distance distribution of bipartite entanglement, combined with local operations and shared randomness, cannot achieve a relevant quantum advantage. Specifically, we prove that these networks do not help in preparing resourceful quantum states such as Greenberger-Horne-Zeilinger states or cluster states, despite the free availability of long-distance entanglement. At an abstract level, our work points towards a fundamental difference between bipartite and multipartite entanglement. From a practical perspective, our results highlight the need for classical communication combined with quantum memories to fully harness the power of quantum networks.
Entanglement distribution is essential for unlocking the potential of distributed quantum information processing. We consider an N-partite network where entanglement is distributed via a central source over lossy channels, and network participants cooperate to establish entanglement between any two chosen parties under local operations and classical communication (LOCC). We develop a general mathematical framework to assess the average bipartite entanglement shared in a lossy distribution, and introduce a tractable lower bound by optimizing over a subset of single-parameter LOCC transformations. Our results show that probabilistically extracting Bell pairs from W states is more advantageous than deterministically extracting them from GHZ-like states in lossy networks, with this advantage increasing with network size. We further extend our analysis analytically, proving that W states remain more effective in large-scale networks. These findings offer valuable insights into the practical deployment of near-term networks, and corroborate a trade-off relationship between the success conversion probability of entanglement distribution protocols and their robustness to loss.
Distribution and distillation of entanglement over quantum networks is a basic task for Quantum Internet applications. A fundamental question is then to determine the ultimate performance of entanglement distribution over a given network. Although this question has been extensively explored for bipartite entanglement-distribution scenarios, less is known about multipartite entanglement distribution. Here we establish the fundamental limit of distributing multipartite entanglement, in the form of GHZ states, over a quantum network. In particular, we determine the multipartite entanglement distribution capacity of a quantum network, in which the nodes are connected through lossy bosonic quantum channels. This setting corresponds to a practical quantum network consisting of optical links. The result is also applicable to the distribution of multipartite secret key, known as common key, for both a fully quantum network and trusted-node based quantum key distribution network. Our results set a general benchmark for designing a network topology and network quantum repeaters (or key relay in trusted nodes) to realize efficient GHZ state/common key distribution in both fully quantum and trusted-node-based networks. We show an example of how to overcome this limit by introducing a network quantum repeater. Our result follows from an upper bound on distillable GHZ entanglement introduced here, called the "recursive-cut-and-merge" bound, which constitutes major progress on a longstanding fundamental problem in multipartite entanglement theory. This bound allows for determining the distillable GHZ entanglement for a class of states consisting of products of bipartite pure states.
A quantum internet aims at harnessing networked quantum technologies, namely by distributing bipartite entanglement between distant nodes. However, multipartite entanglement between the nodes may empower the quantum internet for additional or better applications for communications, sensing, and computation. In this work, we present an algorithm for generating multipartite entanglement between different nodes of a quantum network with noisy quantum repeaters and imperfect quantum memories, where the links are entangled pairs. Our algorithm is optimal for GHZ states with 3 qubits, maximising simultaneously the final state fidelity and the rate of entanglement distribution. Furthermore, we determine the conditions yielding this simultaneous optimality for GHZ states with a higher number of qubits, and for other types of multipartite entanglement. Our algorithm is general also in the sense that it can optimise simultaneously arbitrary parameters. This work opens the way to optimally generate multipartite quantum correlations over noisy quantum networks, an important resource for distributed quantum technologies.