Quantum networks are of high interest nowadays and a quantum internet has been long envisioned. Network-entanglement adapts the notion of entanglement to the network scenario and network-entangled states are considered to be a resource to overcome the limitations of a given network structure. In this work, we introduce measures of quantum network-entanglement that are well-defined within the general framework of quantum resource theories, which at the same time have a clear operational interpretation characterizing the extra resources necessary to prepare a targeted quantum state within a given network. In particular, we define the network communication cost and the network round complexity, which turn out to be intimately related to graph-theoretic parameters. We also provide methods to estimate these measures by introducing novel witnesses of network-entanglement.
Quantum networks are of high interest nowadays and a quantum internet has been long envisioned. Network-entanglement adapts the notion of entanglement to the network scenario and network-entangled states are considered to be a resource to overcome the limitations of a given network structure. In this work, we introduce measures of quantum network-entanglement that are well-defined within the general framework of quantum resource theories, which at the same time have a clear operational interpretation characterizing the extra resources necessary to prepare a targeted quantum state within a given network. In particular, we define the network communication cost and the network round complexity, which turn out to be intimately related to graph-theoretic parameters. We also provide methods to estimate these measures by introducing novel witnesses of network-entanglement.
Entangled quantum networks provide great flexibilities and scalabilities for quantum information processing or quantum Internet. Most of results are focused on the nonlocalities of quantum networks. Our goal in this work is to explore new characterizations of any networks with theory-independent configurations. We firstly prove the configuration inequality for any network using the fractional independent set of the associated graph. These inequalities can be built with polynomial-time complexity. The new result allows featuring correlations of any classical network depending only on its network topology. Similar inequalities hold for all entangled quantum networks with any local measurements. This shows an inherent feature of quantum networks under local unitary operations. It is then applied for verifying almost all multipartite entangled pure states with linear complexity, and witnessing quantum network topology without assumption of inputs. The configuration theory is further extended for any no-signalling networks. These results may be interesting in entanglement theory, quantum information processing, and quantum networks.
The Quantum Internet is commonly envisioned as a network that transports quantum states and distributes entanglement as the key resource underpinning distributed quantum applications. This view is necessary but incomplete if quantum phenomena are confined to what the network carries or manages, while network functionalities remain grounded predominantly in classical abstractions. This Perspective advances a broader thesis: quantum phenomena can also participate directly in the realization of network functionalities. We first establish the architectural baseline by introducing entanglement as a stateful network resource whose operational condition is non-locally distributed across remote nodes, evolves through manipulation or consumption, and degrades over time through decoherence. Its evolving state must therefore remain visible to the functionalities acting on it. We then move beyond resource visibility and use two mechanisms as proof points of a broader quantum-native functional design space: entanglement generation during propagation through coherent spatial-path superposition, and operational connectivity induced by shared entanglement that can depart from the physical graph. These examples show that paths, neighbors, or participating nodes may become operationally relevant in ways determined by quantum coherence and shared entanglement, rather than by physical connectivity alone. We identify Quantum Addressing as a transversal abstraction capable of representing such relations while complementing, rather than replacing, classical addressing and signaling. The resulting perspective broadens the Quantum Internet from transporting quantum information and distributing entanglement to exploiting quantum phenomena in network functioning, opening a coupled frontier spanning routing, forwarding, control, and functionality placement.
Abstract We define metrics and measures to characterize the ratio of accessible quantum entanglement for complex network failures in the quantum Internet. A complex network failure models a situation in the quantum Internet in which a set of quantum nodes and a set of entangled connections become unavailable. A complex failure can cover a quantum memory failure, a physical link failure, an eavesdropping activity, or any other random physical failure scenarios. Here, we define the terms such as entanglement accessibility ratio, cumulative probability of entanglement accessibility ratio, probabilistic reduction of entanglement accessibility ratio, domain entanglement accessibility ratio, and occurrence coefficient. The proposed methods can be applied to an arbitrary topology quantum network to extract relevant statistics and to handle the quantum network failure scenarios in the quantum Internet.
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.
Abstract The realization of a desirably functional quantum Internet is hindered by fundamental and practical challenges such as high loss during transmission of quantum systems, decoherence due to interaction with the environment, and fragility of quantum states under measurement. We study the implications of these constraints by analyzing the limitations on the scaling and robustness of the quantum Internet. Considering quantum networks, we present practical bottlenecks for secure communication, delegated computing, and resource distribution among end nodes. In particular, we show that the device-independent quantum key distribution (DI-QKD) network of isotropic states with parameter p has a finite diameter depending on p . Motivated by the power of abstraction in graph theory (in association with quantum information theory), that allows us to consider the topology of a network of users spatially separated over long distances around the globe or separated as nodes within the small space over a processor or circuit within a same framework, we consider graph-theoretic quantifiers to assess network robustness and provide critical values of communication lines for viable communication over quantum Internet. We consider some quantum networks of practical interest, ranging from satellite-based networks connecting far-off spatial locations to currently available quantum processor architectures within computers, and analyze their robustness to perform quantum information processing tasks. Some of these tasks form primitives for delegated quantum computing, e.g., entanglement distribution and quantum teleportation, that are desirable for all scale of quantum networks, be it quantum processors or quantum Internet.