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arXiv:2603.29601

Quantum connectivity of quantum networks

Md Sohel Mondal, Shashank Shekhar, Siddhartha Santra

quant-phSubmitted Mar 31, 2026• Announced Apr 1, 2026• 0 citations
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Abstract

The practical utility of a quantum network depends on its ability to establish entanglement between arbitrary node pairs with quality sufficient to execute entanglement enabled tasks. This capability can be assessed globally, through aggregate performance over all node pairs, as well as locally, at the level of individual nodes. Since entanglement-based connections form a layer above the underlying physical topology, quantum connectivity is not adequately captured by classical topological connectivity metrics. To enable characterisation of the quantum connectivity at the level of the network (or its subnetworks), we introduce the quantum connectivity measure (QCM), which quantifies the average connection quality between pairs of network nodes. Further, we describe two quantities, the quantum-connected fraction (QCF) and the quantum clustering coefficient (QCC), naturally derived from the QCM, which capture important features of the functional connectivity of the quantum network at the level of the network and an individual node, respectively. These metrics of quantum connectivity depend crucially on the entanglement distribution protocol and the quantum network parameters in addition to its physical topology. We demonstrate the crucial distinction between topological and quantum connectivity, showing that even a fully connected graph can be functionally disconnected for quantum tasks if average network edge-concurrence falls below a critical threshold. These quantum connectivity metrics thus provide important tools for the design, optimization, and benchmarking of future quantum networks.

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•Jan 1, 2010•6 citations
The practical utility of a quantum network depends on its ability to establish entanglement between arbitrary node pairs with quality sufficient to execute entanglement enabled tasks. This capability can be assessed globally, through aggregate performance over all node pairs, as well as locally, at the level of individual nodes. Since entanglement-based connections form a layer above the underlying physical topology, quantum connectivity is not adequately captured by classical topological connectivity metrics. To enable characterisation of the quantum connectivity at the level of the network (or its subnetworks), we introduce the quantum connectivity measure (QCM), which quantifies the average connection quality between pairs of network nodes. Further, we describe two quantities, the quantum-connected fraction (QCF) and the quantum clustering coefficient (QCC), naturally derived from the QCM, which capture important features of the functional connectivity of the quantum network at the level of the network and an individual node, respectively. These metrics of quantum connectivity depend crucially on the entanglement distribution protocol and the quantum network parameters in addition to its physical topology. We demonstrate the crucial distinction between topological and quantum connectivity, showing that even a fully connected graph can be functionally disconnected for quantum tasks if average network edge-concurrence falls below a critical threshold. These quantum connectivity metrics thus provide important tools for the design, optimization, and benchmarking of future quantum networks.
Large-scale quantum networks, necessary for distributed quantum information processing, are posited to have quantum entangled systems between distant network nodes. The extent and quality of distributed entanglement in a quantum network, that is its functionality, depends on its topology, edge-parameter distributions and the distribution protocol. We uncover the parametric entanglement topography and introduce the notion of typical and maximal viable regions for entanglement-enabled tasks in a general model of large-scale quantum networks. We show that such a topographical analysis, in terms of viability regions, reveals important functional information about quantum networks, provides experimental targets for the edge parameters and can guide efficient quantum network design. Applied to a photonic quantum network, such a topographical analysis shows that in a network with radius 10310^3103 kms and 1500 nodes, arbitrary pairs of nodes can establish quantum secure keys at a rate of Rsec=1R_{sec}=1Rsec​=1 kHz using 111 MHz entanglement generation sources on the edges and as few as 3 entanglement swappings at intermediate nodes along network paths.
Abstract We study entanglement percolation in qubit-based planar quantum network models of arbitrary topology, where neighboring nodes are initially connected by pure states with quenched disorder in their entanglement. To address this, we develop a physics-informed heuristic algorithm designed to find a sequence of entanglement swapping and distillation operations to connect any pair of distant nodes. The algorithm combines locally optimal percolation strategies between nodes at a maximum distance of one swapping operation. If this fails to produce a maximally entangled state, it looks for alternative paths surrounding intermediate states within the process. We analytically find and numerically verify thresholds in quantum percolation, which depend on the initial network configuration and entanglement, and are associated with specific percolation strategies. We classify these strategies based on the connectivity, a quantity that relates the entanglement in the final state and the level of integrity of the network at the end of the process. We find distinct regimes of quantum percolation, which are clearly separated by the percolation thresholds of the employed strategies and vastly vary according to the network topology.
The topology of classical networks is determined by physical links between nodes, and after a network request the links are used to establish the desired connections. Quantum networks offer the possibility to generate different kinds of entanglement prior to network requests, which can substitute links and allow one to fulfill multiple network requests with the same resource state. We utilize this to design entanglement-based quantum networks tailored to their desired functionality, independent of the underlying physical structure. The kind of entanglement to be stored is chosen to fulfill all desired network requests (i.e. parallel bipartite or multipartite communications between specific nodes chosen from some finite set), but in such a way that the storage requirement is minimized. This can be accomplished by using multipartite entangled states shared between network nodes that can be transformed by local operations to different target states. We introduce a clustering algorithm to identify connected clusters in the network for a given desired functionality, i.e. the required network topology of the entanglement-based network, and a merging algorithm that constructs multipartite entangled resource states with reduced memory requirement to fulfill all desired network requests. This leads to a significant reduction in required time and resources, and provides a powerful tool to design quantum networks that is unique to entanglement-based networks.
Abstract The entanglement properties of quantum states associated with directed graphs are investigated. Using a measure derived from the Fubini–Study metric, multipartite entanglement is quantitatively related to the local connectivity of the graph. In Entanglement in Directed Graph States (2025), arXiv:2505.10716, it is demonstrated that the vertex degree distribution fully determines this entanglement measure and remains invariant under vertex relabeling, highlighting its topological character. As a consequence, the measure depends only on the total degree of each vertex, making it independent of the distinction between incoming and outgoing edges. This framework is applied to several specific graph structures, including hierarchical networks, neural network–inspired graphs, full binary tree and linear bridged cycle graphs, demonstrating how their combinatorial properties influence entanglement distribution. These results provide a geometric perspective on quantum correlations in complex systems, offering potential applications in the design and analysis of quantum networks.
Quantum network is fragile to disturbances when qubits are transmitted through quantum channel. Reliability is an essential requirement for a quantum network and even the future quantum internet. A metric is needed to describe the reliability of a quantum network to build a robust infrastructure and communication protocols. In this work, we combined quantum physical parameters with graphic algebraic connectivity to indicate the transmission throughput of a grid quantum network. This metric can be extended to multiple equal point-to-point distance topology. This work also studies how to tune specific physical parameters to maintain or even increase connectivity when nodes or edges are removed from a network. Using this metric, resources consumption are compared.
This Thesis contributes to the theory of entanglement distribution in quantum networks, analyzing the generation of long-distance entanglement in particular.We consider that neighboring stations share one partially entangled pair of qubits, which emphasizes the difficulty of creating remote entanglement in realistic settings.The task is then to design local quantum operations at the stations, such that the entanglement present in the links of the whole network gets concentrated between few parties only, regardless of their spatial arrangement.First, we study quantum networks with a two-dimensional lattice structure, where quantum connections between the stations (nodes) are described by non-maximally entangled pure states (links).We show that the generation of a perfectly entangled pair of qubits over an arbitrarily long distance is possible if the initial entanglement of the links is larger than a threshold.This critical value highly depends on the geometry of the lattice, in particular on the connectivity of the nodes, and is related to a classical percolation problem.We then develop a genuine quantum strategy based on multipartite entanglement, improving both the threshold and the success probability of the generation of long-distance entanglement.Second, we consider a mixed-state definition of the connections of the quantum networks.This formalism is well-adapted for a more realistic description of systems in which noise (random errors) inevitably occurs.New techniques are required to create remote entanglement in this setting, and we show how to locally extract and globally process some error syndromes in order to create useful long-distance quantum correlations.Finally, we turn to networks that have a complex topology, which is the case for most real-world communication networks such as the Internet for instance.Besides many other characteristics, these systems have in common the small-world feature, stating that any two nodes are separated by a few links only.Based on the theory of random graphs, we propose a model of quantum complex networks, which exhibit some totally unexpected properties compared to their classical counterparts.5.1 Propagation of a large GHZ state through the lattice . . .5.2 Bit-flip error correction . . . . . . . . . . . . .