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arXiv:2003.05239 · Quantum Information Processing

Entanglement accessibility measures for the quantum Internet

László Gyöngyösi, Sándor Imre

Published Feb 15, 2020• 30 citations
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Abstract

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.

DOI
10.1007/s11128-020-2605-y

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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.
Quantum entanglement is a crucial element of establishing the entangled network structure of the quantum Internet. Here we define a method to achieve controlled entanglement access in the quantum Internet. The proposed model defines different levels of entanglement accessibility for the users of the quantum network. The path cost is determined by an integrated criterion on the entanglement fidelities between the quantum nodes and the probabilities of entangled connections of an entangled path. We reveal the connection between the number of available entangled paths and the accessible fidelity of entanglement and reliability in the end nodes. The scheme provides an efficient model for entanglement access control in the experimental quantum Internet.
Quantum entanglement is a building block of the entangled quantum networks of the quantum Internet. A fundamental problem of the quantum Internet is entanglement distribution. Since quantum entanglement will be fundamental to any future quantum networking scenarios, the distribution mechanism of quantum entanglement is a critical and emerging issue in quantum networks. Here we define the method of opportunistic entanglement distribution for the quantum Internet. The opportunistic model defines distribution sets that are aimed to select those quantum nodes for which the cost function picks up a local minimum. The cost function utilizes the error patterns of the local quantum memories and the predictability of the evolution of the entanglement fidelities. Our method provides efficient entanglement distributing with respect to the actual statuses of the local quantum memories of the node pairs. The model provides an easily-applicable, moderate-complexity solution for high-fidelity entanglement distribution in experimental quantum Internet scenarios.
Abstract Quantum networks allow us to harness networked quantum technologies and to develop a quantum internet. But how robust is a quantum network when its links and nodes start failing? We show that quantum complex networks based on typical noisy quantum-repeater nodes are prone to discontinuous phase transitions with respect to the random loss of operating links and nodes, abruptly compromising the connectivity of the network, and thus significantly limiting the reach of its operation. Furthermore, we determine the critical quantum-repeater efficiency necessary to avoid this catastrophic loss of connectivity as a function of the network topology, the network size, and the distribution of entanglement in the network. From all the network topologies tested, a scale-free network topology shows the best promise for a robust large-scale quantum internet.
Quantum networks establish end-to-end quantum communication by utilizing probabilistic quantum processes, including entanglement distribution between remote nodes and entanglement swapping at repeater nodes. While previous studies have aimed to maximize the number of entanglement connections under the probabilistic nature, physical link failures provide an additional challenge to ensuring consistent entanglement connections. To address this issue, a path provisioning model should be designed to maintain a high entanglement path success probability even in the presence of link failure. This paper proposes a provisioning model to find link- disjoint entanglement paths in quantum networks, considering both link-level transmission success probabilities and node-level entanglement swapping success probabilities. The objective of the proposed model is to maximize the entanglement path success probability for survivability under link failure. We formulate this model as an integer linear programming problem. The numerical results indicate that the proposed model achieves higher survivability than baseline algorithms.
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.
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.