Analysis of Multipartite Entanglement Distribution using a Central Quantum-Network Node

Avis, Guus; Rozpędek, Filip; Wehner, Stephanie

doi:10.48550/arxiv.2203.05517

Cited by 3 publications

(5 citation statements)

References 106 publications

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“…In general, the distance in an Erdős-Rényi network grows logarithmically with the network size, or even sub-logarithmically, as a consequence of the smallworld effect [31]. Substituting in (8), one obtains a more detailed upper-bound:…”

Section: Simulation Resultsmentioning

confidence: 99%

“…In order to take full advantage of these technologies the next natural step is to have a quantum network capable of distributing entanglement between any two quantum terminals, or even more demanding, between multiple parties at the same time, called multipartite entanglement, and sometimes seen as a form of quantum multicast [6]. The work in [7] considers multipartite entanglement assuming no existence of quantum memories, while [8] assumes they exist at the nodes. Quantum networks should connect multiple quantum computers in order to scale up quantum computing.…”

Section: Introductionmentioning

confidence: 99%

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Shortest Path Finding in Quantum Networks With Quasi-Linear Complexity

et al. 2023

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A fully-quantum network implies the creation of quantum entanglement between a given source node and some other destination node, with a number of quantum repeaters in between. This paper tackles the problem of quantum entanglement distribution by solving the routing problem over an infrastructure based on quantum repeaters and with a finite number of pairs of entangled qubits available in each link. The network model considers that link purification is available such that a nested purification protocol can be applied at each link to generate entangled qubits with higher fidelity than the original ones. A low-complexity multiobjective routing algorithm to find the shortest path between any two given nodes is proposed and assessed for random networks, using a fairly general path extension mechanism that can fit a large family of particular technological requirements. Different types of quantum protocols require different levels of fidelity for the entangled qubit pairs. For that reason, the proposed algorithm identifies the shortest path between two nodes that assures an end-to-end fidelity above a specified threshold. The minimum requirements for the end-toend entanglement fidelity depend on the whole extension of the paths, and cannot be looked at as a local property of each link. Moreover, one needs to keep track not only of the shortest path, but also of longer paths holding more entangled qubits than the shorter paths in order to satisfy the fidelity criterion. Thus, standard single parameter shortest-path algorithms do not necessarily converge to the optimal solution. The problem of finding the best path in a network subject to multiple criteria (known as multi-objective routing) is, in general, an NP-hard problem due to the rapid growth of the number of stored paths. This work proposes a metric that identifies and discards paths that are objectively worse than others. By doing so, the time complexity of the proposed algorithm scales near-to-linearly with respect to the number of nodes in the network, showing that the shortest-path problem in quantum networks can be solved with a complexity very close to the one of the classical counterparts. That is analytically proved for the case where all the links of a path have the same fidelity (homogeneous model). The algorithm is also adapted to a particular type of path extension, where different links along a path can be purified to different degrees, asserting its flexibility and near-to-linearity even when heterogeneous fidelities along the sections of a path are considered.INDEX TERMS Quantum networks, quantum repeaters, path-finding algorithm, end-to-end fidelity, multiobjective routing.The associate editor coordinating the review of this manuscript and approving it for publication was Bijoy Chand Chatterjee .

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Section: Simulation Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Shortest Path Finding in Quantum Networks With Quasi-Linear Complexity

et al. 2023

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“…Nonetheless, doing so is compatible with our methodology, still providing a guarantee of optimality. This same methodology could then be applied to different models of networks, for example having some nodes capable of distributing multipartite entanglement [51], or different distribution schemes [52], introducing entanglement purification rounds in the bipartite distribution scheme [33], or even different quantum repeater protocols [53], providing a starting point to optimally generate multipartite entanglement over noisy quantum networks.…”

Section: Discussionmentioning

confidence: 99%

Distributing Multipartite Entanglement over Noisy Quantum Networks

Bugalho

Coutinho

Monteiro

et al. 2023

Quantum

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A quantum internet aims at harnessing networked quantum technologies, namely by distributing bipartite entanglement between distant nodes. However, multipartite entanglement between the nodes may empower the quantum internet for additional or better applications for communications, sensing, and computation. In this work, we present an algorithm for generating multipartite entanglement between different nodes of a quantum network with noisy quantum repeaters and imperfect quantum memories, where the links are entangled pairs. Our algorithm is optimal for GHZ states with 3 qubits, maximising simultaneously the final state fidelity and the rate of entanglement distribution. Furthermore, we determine the conditions yielding this simultaneous optimality for GHZ states with a higher number of qubits, and for other types of multipartite entanglement. Our algorithm is general also in the sense that it can optimise simultaneously arbitrary parameters. This work opens the way to optimally generate multipartite quantum correlations over noisy quantum networks, an important resource for distributed quantum technologies.

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“…Entanglement swapping is employed in nodes in the EPR chains to establish long-haul EPR pairs between the central node and the terminals. Thereafter, through local adjustments of these long-haul EPR pair connections, the central node can effectively transmit its multipartite entangled state to the remote clients [14,15]. This central node approach is schematized in figure 4.…”

Section: Other Models For Multipartite Entanglement Distributionmentioning

confidence: 99%

“…Many of these protocols involve the initial distribution of Bell pair states, followed by local operations at repeater nodes. This process ultimately establishes connections between clients and a central node for teleporting the desired graph state, as elaborated in [14] and [15]. In today's quantum networks, repeater nodes typically perform a single function: forwarding or swapping bipartite entanglement.…”

Section: Introductionmentioning

confidence: 99%

The quantum internet: an efficient stabilizer states distribution scheme

Koudia

2023

Phys. Scr.

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Quantum networks are a fundamental component of quantum technologies, playing a pivotal role in advancing distributed quantum computing and laying the groundwork for the future quantum internet. They offer a scalable modular architecture for quantum chips and support infrastructure for measurement-based quantum computing. Furthermore, quantum networks serve as the backbone of the quantum internet, ensuring high levels of security. Notably, the advantages of quantum networks in communication are contingent upon entanglement distribution, which faces challenges such as high latency in protocols relying on Bell pair distribution and bipartite entanglement swapping. Additionally, algorithms designed for multipartite entanglement routing encounter intractability issues, rendering them unsolvable within polynomial time. In this paper, we explore a novel approach to distribute graph states in quantum networks, leveraging local quantum coding (LQC) isometries and multipartite states transfer. We also present single-use bounds for stabilizer states distribution. Analogous to network coding, these bounds are attainable when appropriate isometries and stabilizer codes are selected for relay nodes, resulting in reduced latency in entanglement distribution. We further demonstrate the protocol’s advantages across various network performance metrics.

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Analysis of Multipartite Entanglement Distribution using a Central Quantum-Network Node

Cited by 3 publications

References 106 publications

Shortest Path Finding in Quantum Networks With Quasi-Linear Complexity

Shortest Path Finding in Quantum Networks With Quasi-Linear Complexity

Distributing Multipartite Entanglement over Noisy Quantum Networks

The quantum internet: an efficient stabilizer states distribution scheme

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