Entanglement-Based Artificial Topology: Neighboring Remote Network Nodes

TL;DR

This work reframes inter-network connectivity in quantum networks by leveraging multipartite entanglement to create a dynamically adjustable artificial topology between two QLANs. The authors propose a binary star graph state $|S_{n_1,n_2}\rangle$ distributed across the two QLANs, built from intra-QLAN star states and a single inter-QLAN EPR, enabling inter-QLAN links via local operations only. They classify several traffic-driven artificial topologies—hierarchical peer-to-peer, pure peer-to-peer, role delegation, and extranet—demonstrating that these LU-equivalent graphs can be realized by local Pauli measurements and single-qubit gates without additional quantum communication. This approach provides a proactive, traffic-aware connectivity paradigm that can adapt to varying demands, potentially improving inter-QLAN communication while maintaining low physical-resource requirements. The work also outlines future directions on noise resilience, scalability, and simulation in realistic network scenarios.

Abstract

Entanglement is unanimously recognized as the key communication resource of the Quantum Internet. Yet, the possibility of implementing novel network functionalities by exploiting the marvels of entanglement has been poorly investigated so far, by mainly restricting the attention to bipartite entanglement. Conversely, in this paper, we aim at exploiting multipartite entanglement as inter-network resource. Specifically, we consider the interconnection of different Quantum Local Area Networks (QLANs), and we show that multipartite entanglement allows to dynamically generate an inter-QLAN artificial topology, by means of local operations only, that overcomes the limitations of the physical QLAN topologies. To this aim, we first design the multipartite entangled state to be distributed within each QLAN. Then, we show how such a state can be engineered to: i) interconnect nodes belonging to different QLANs, and ii) dynamically adapt to different inter-QLAN traffic patterns. Our contribution aims at providing the network engineering community with a hands-on guideline towards the concept of artificial topology and artificial neighborhood.

Figures (22)

• Figure 1: Schematic representation of the considered physical quantum network architecture. The network comprises several QLANs. Within each QLAN, a super-node generates and distributes resources -- namely, multipartite entangled states -- to a set of quantum nodes -- referred to as clients -- with a star-like topology. Inter-QLAN connectivity is enabled by point-to-point quantum channels interconnecting different super-nodes. For the sake of illustration consistency, we maintain the super-node and client node icons used in this figure also in the following figures.
• Figure 2: Schematic diagram of the correspondence between graph domain and graph state domain, i.e, of the mapping between projective measurements through Pauli operators on graph states and transformations of the associated graphs.
• Figure 3: Pictorial representation of the multipartite entanglement distribution process within a single QLAN of Fig. \ref{['fig:01']}. (a) The super-node is responsible for entanglement generation and distribution within each QLAN. Accordingly, it locally generates the multipartite entanglement state and distribute it via teleportation. For this, one EPR pair per client must be generated at the super-node. (b) Once an EPR pair is shared between super-node and each client, one e-bit of the multipartite entangled state can be teleported to the client by consuming such an EPR. (c) Eventually, the multipartite entangled state is distributed to the clients so that all the QLAN nodes, including the super-node, are entangled.
• Figure 4: Path graph $P_n$.
• Figure 5: Even Cycle graph $C_{2k}$.

Theorems & Definitions (30)

• Remark
• Definition 1: Neighborhood
• Definition 2: Induced Subgraph
• Definition 3: Complete Graph
• Definition 4: Graph Complementation
• Definition 5: Local Complementation
• Definition 6: Vertex Deletion
• Remark
• Definition 7: LU equivalence
• Remark