Quantum networks illustrate the use of connected nodes of quantum systems as the backbone of distributed quantum information processing. When the network nodes are entangled in graph states, such a quantum platform is indispensable to almost all the existing distributed quantum tasks. Unfortunately, real networks unavoidably suffer from noise and technical restrictions, making nodes transit from quantum to classical at worst. Here, we introduce a figure of merit in terms of the number of classical nodes for quantum networks in arbitrary graph states. Such a network property is revealed by exploiting a novel Einstein-Podolsky-Rosen steerability. Experimentally, we demonstrate photonic quantum networks of n_{q} quantum nodes and n_{c} classical nodes with n_{q} up to 6 and n_{c} up to 18 using spontaneous parametric down-conversion entanglement sources. We show that the proposed method is faithful in quantifying the classical defects in prepared multiphoton quantum networks. Our results provide novel identification of generic quantum networks and nonclassical correlations in graph states.
Quantum networks illustrate the use of connected nodes of quantum systems as the backbone of distributed quantum information processing. When the network nodes are entangled in graph states, such a quantum platform is indispensable to almost all the existing distributed quantum tasks. Unfortunately, real networks unavoidably suffer from noise and technical restrictions, making nodes transit from quantum to classical at worst. Here, we introduce a figure of merit in terms of the number of classical nodes for quantum networks in arbitrary graph states. Such a network property is revealed by exploiting a novel Einstein-Podolsky-Rosen steerability. Experimentally, we demonstrate photonic quantum networks of n_{q} quantum nodes and n_{c} classical nodes with n_{q} up to 6 and n_{c} up to 18 using spontaneous parametric down-conversion entanglement sources. We show that the proposed method is faithful in quantifying the classical defects in prepared multiphoton quantum networks. Our results provide novel identification of generic quantum networks and nonclassical correlations in graph states.
Quantum networks comprised of entangled end nodes serve stronger than the classical correlation for unparalleled quantum internet applications. However, practical quantum networking is affected by noise, which at its worst, causes end nodes to be described by pre-existing classical data. In such untrusted networks, determining quantum network fidelity and genuine multi-node entanglement becomes crucial. Here, we show that determining quantum network fidelity and genuine N -node entanglement in an untrusted star network requires only N + 1 measurement settings. This method establishes a semi-trusted framework, allowing some nodes to relax their assumptions. Our network determination method is enabled by detecting genuine N -node Einstein-Podolsky-Rosen steerability. Experimentally, using spontaneous parametric down-conversion entanglement sources, we demonstrate the determinations of genuine 3-photon and 4-photon quantum networks and the false positives of the widely used entanglement witness, the fidelity criterion of 1/2. Our results provide a scalable method for the determination of multipartite entanglement in realistic quantum networks.
Quantum networks (QNs) are expected to play a key role in next-generation networks. A QN is comprised of quantum nodes and links (or bonds) representing entangled qubit pairs (EQPs) shared between two nodes. The probability of establishing a pure maximally entangled pair, known as Einstein-Podolsky-Rosen (EPR) pair, between two neighboring nodes represents the linking probability (or bond occupation probability). If such probability exceeds the so-called percolation threshold, the QN exhibits a percolation phenomenon characterized by the emergence of a giant cluster spanning the entire network. In the presence of such a giant cluster, any two arbitrary nodes in the system are connected by a chain of links with a non-zero probability, thus establishing EPR pairs at remote nodes. This work introduces a procedure for obtaining QNs from initially isolated quantum nodes. In the proposed procedure, two copies of EPR pairs are prepared at a source node and two qubits, one from each pair, are sent to a neighboring node through a noisy quantum channel. Then, a pair of mixed quantum states is established between the source node and the neighboring node. By performing local operations and classical communication, an EPR pair can be established between these two nodes with non-zero probability. Repeating this procedure for every pair of source node and neighboring node, a QN exhibiting a percolation phenomenon can be obtained.
Quantum network is a set of nodes connected with channels, through which the nodes communicate photons and classical information. Classical structural complexity of a quantum network may be defined through its physical structure, i.e. mutual position of nodes and channels connecting them. We show here that the classical structural complexity of a quantum network does not restrict the structural complexity of entanglement graphs, which may be created in the quantum network with local operations and classical communication. We show, in particular, that 1D quantum network can simulate both simple entanglement graphs such as lattices and random graphs and complex small-world graphs.
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 103 kms and 1500 nodes, arbitrary pairs of nodes can establish quantum secure keys at a rate of Rsec=1 kHz using 1 MHz entanglement generation sources on the edges and as few as 3 entanglement swappings at intermediate nodes along network paths.
In recent years, quantum communication and quantum computing have become strategic technologies of great importance to countries around the world, with profound implications for individuals, businesses, and even nations. Among these, graph states are a very important class of multi-particle entangled states, playing a crucial role in fields such as quantum secret sharing, measurement-based quantum computing, and quantum metrology. However, the distribution of graph states faces the following challenges: existing quantum communication networks designed for single-qubit transmission cannot effectively accomplish graph state distribution tasks, and current methods for graph state distribution lack consideration of node resources, making it difficult to complete graph state distribution in some cases.We conduct research on cross-node graph states distribution methods in quantum communication networks under limited resource constraints. To address the issue that current quantum communication networks cannot handle graph states and other multi-particle entangled states, a graph state distribution method is proposed. This method combines local operations and classical communication to meet the distribution requirements for graph states, which are multi-particle entangled states. Additionally, to solve the problem of limited quantum resources at individual nodes, we proposed a graph states segmentation method. This method divides a complete graph state into subgraphs for distribution and subsequently integrates them, enabling graph state distribution services in a broader range of resource scenarios.