We consider the problem of generating multipartite entangled states in a quantum network upon request. We follow a top-down approach, where the required entanglement is initially present in the network in form of network states shared between network devices, and then manipulated in such a way that the desired target state is generated. This minimizes generation times, and allows for network structures that are in principle independent of physical links. We present a modular and flexible architecture, where a multi-layer network consists of devices of varying complexity, including quantum network routers, switches and clients, that share certain resource states. We concentrate on the generation of graph states among clients, which are resources for numerous distributed quantum tasks. We assume minimal functionality for clients, i.e. they do not participate in the complex and distributed generation process of the target state. We present architectures based on shared multipartite entangled Greenberger-Horne-Zeilinger (GHZ) states of different size, and fully connected decorated graph states respectively. We compare the features of these architectures to an approach that is based on bipartite entanglement, and identify advantages of the multipartite approach in terms of memory requirements and complexity of state manipulation. The architectures can handle parallel requests, and are designed in such a way that the network state can be dynamically extended if new clients or devices join the network. For generation or dynamical extension of the network states, we propose a quantum network configuration protocol, where entanglement purification is used to establish high-fidelity states. The latter also allows one to show that the entanglement generated among clients is private, i.e. the network is secure.
We consider the problem of generating multipartite entangled states in a quantum network upon request. We follow a top-down approach, where the required entanglement is initially present in the network in form of network states shared between network devices, and then manipulated in such a way that the desired target state is generated. This minimizes generation times, and allows for network structures that are in principle independent of physical links. We present a modular and flexible architecture, where a multi-layer network consists of devices of varying complexity, including quantum network routers, switches and clients, that share certain resource states. We concentrate on the generation of graph states among clients, which are resources for numerous distributed quantum tasks. We assume minimal functionality for clients, i.e. they do not participate in the complex and distributed generation process of the target state. We present architectures based on shared multipartite entangled Greenberger-Horne-Zeilinger (GHZ) states of different size, and fully connected decorated graph states respectively. We compare the features of these architectures to an approach that is based on bipartite entanglement, and identify advantages of the multipartite approach in terms of memory requirements and complexity of state manipulation. The architectures can handle parallel requests, and are designed in such a way that the network state can be dynamically extended if new clients or devices join the network. For generation or dynamical extension of the network states, we propose a quantum network configuration protocol, where entanglement purification is used to establish high-fidelity states. The latter also allows one to show that the entanglement generated among clients is private, i.e. the network is secure.
We consider the problem of generating multipartite entangled states in a quantum network upon request. We follow a top-down approach, where the required entanglement is initially present in the network in form of network states shared between network devices, and then manipulated in such a way that the desired target state is generated. This minimizes generation times, and allows for network structures that are in principle independent of physical links. We present a modular and flexible architecture, where a multi-layer network consists of devices of varying complexity, including quantum network routers, switches and clients, that share certain resource states. We concentrate on the generation of graph states among clients, which are resources for numerous distributed quantum tasks. We assume minimal functionality for clients, i.e. they do not participate in the complex and distributed generation process of the target state. We present architectures based on shared multipartite entangled Greenberger–Horne–Zeilinger states of different size, and fully connected decorated graph states, respectively. We compare the features of these architectures to an approach that is based on bipartite entanglement, and identify advantages of the multipartite approach in terms of memory requirements and complexity of state manipulation. The architectures can handle parallel requests, and are designed in such a way that the network state can be dynamically extended if new clients or devices join the network. For generation or dynamical extension of the network states, we propose a quantum network configuration protocol, where entanglement purification is used to establish high fidelity states. The latter also allows one to show that the entanglement generated among clients is private, i.e. the network is secure.
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.
We introduce a repeater scheme to efficiently distribute multipartite entangled states in a quantum network with optimal scaling. The scheme allows to generate graph states such as 2D and 3D cluster states of growing size or GHZ states over arbitrary distances, with a constant overhead per node/channel that is independent of the distance. The approach is genuine multipartite, and is based on the measurement-based implementation of multipartite hashing, an entanglement purification protocol that operates on a large ensemble together with local merging/connection of elementary building blocks. We analyze the performance of the scheme in a setting where local or global storage is limited, and compare it to bipartite and hybrid approaches that are based on the distribution of entangled pairs. We find that the multipartite approach offers a storage advantage, which results in higher efficiency and better performance in certain parameter regimes. We generalize our approach to arbitrary network topologies and different target graph states.
We present a stack model for breaking down the complexity of entanglement-based quantum networks.More specifically, we focus on the structures and architectures of quantum networks and not on concrete physical implementations of network elements.We construct the quantum network stack in a hierarchical manner comprising several layers, similar to the classical network stack, and identify quantum networking devices operating on each of these layers.The layers responsibilities range from establishing point-to-point connectivity, over intra-network graph state generation, to inter-network routing of entanglement.In addition we propose several protocols operating on these layers.In particular, we extend the existing intra-network protocols for generating arbitrary graph states to ensure reliability inside a quantum network, where here reliability refers to the capability to compensate for devices failures.Furthermore, we propose a routing protocol for quantum routers which enables the generation of arbitrary graph states across network boundaries.This protocol, in correspondence with classical routing protocols, can compensate dynamically for failures of routers, or even complete networks, by simply re-routing the given entanglement over alternative paths.We also consider how to connect quantum routers in a hierarchical manner to reduce complexity, as well as reliability issues arising in connecting these quantum networking devices.
Multipartite entangled states are great resources for quantum networks. In this work, we study the distribution, or routing, of entangled states over fixed, but arbitrary, physical networks. Our simplified model represents each use of a quantum channel as the sharing of a Bell pair; local operations and classical communications are considered to be free. We introduce two protocols to distribute, respectively, Greenberger-Horne-Zeilinger (GHZ) states and arbitrary graph states over arbitrary quantum networks. The GHZ states' distribution protocol takes a single step and is optimal in terms of the number of Bell pairs used; the graph states' distribution protocol uses, at most, twice as many Bell pairs and steps as the optimal routing protocol for the worst-case scenario.
The effective routing of entanglement over a quantum network is a fundamental problem in quantum communication. The distribution and reshaping of multipartite entanglement over a quantum network requires scalable protocols that adapt to the underlying topology. Graph states provide a convenient framework for this challenging task, as they encode global entanglement in a structured way that can be locally manipulated to produce a variety of target states, without requiring additional long-distance quantum operations. In this article, we propose graph-state-based routing protocols for sharing GHZ states, achieving larger sizes than those achieved in the existing works for given network topologies. For this improvement, we consider tree structures connecting the users participating in the final GHZ states, as opposed to the linear configurations used in the earlier works. In particular, for grid networks, we show special constructions of such trees that achieve larger GHZ states than the prior works. Moreover, if the user nodes along which the entanglement is to be routed are pre-specified, a strategy is proposed to accomplish this routing.