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IEEE Globecom Workshops (GC Wkshps)

End-to-End Entanglement Rate: Toward a Quantum Route Metric

Marcello Caleffi

Published Dec 1, 2017• 34 citations
Publisher

Abstract

We present an entanglement-generation rate analysis for generic quantum network architectures composed by repeaters operating through single atoms in optical cavities. Specifically, we analytically derive the end-to-end entanglement rate between a couple of nodes through an arbitrary path. To this aim, we first model the entanglement generation through a stochastic framework that allows us to jointly account for all the key physical-mechanisms affecting the end-to-end entanglement rate, such as decoherence time, atom- photon and photon-photon entanglement generation, entanglement swapping and imperfect bell-state measurement. Then, we derive the closed-form expression of the end-to-end entanglement rate. Finally, we evaluate the entanglement rate under realistic parameter setting.

DOI
10.1109/glocomw.2017.8269080

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We present an entanglement-generation rate analysis for generic quantum network architectures composed by repeaters operating through single atoms in optical cavities. Specifically, we analytically derive the end-to-end entanglement rate between a couple of nodes through an arbitrary path. To this aim, we first model the entanglement generation through a stochastic framework that allows us to jointly account for all the key physical-mechanisms affecting the end-to-end entanglement rate, such as decoherence time, atom- photon and photon-photon entanglement generation, entanglement swapping and imperfect bell-state measurement. Then, we derive the closed-form expression of the end-to-end entanglement rate. Finally, we evaluate the entanglement rate under realistic parameter setting.
To fully unleash the potentials of quantum computing, several new challenges and open problems need to be addressed. From a routing perspective, the optimal routing problem, i.e., the problem of jointly designing a routing protocol and a route metric assuring the discovery of the route providing the highest quantum communication opportunities between an arbitrary couple of quantum devices, is crucial. In this paper, the optimal routing problem is addressed for generic quantum network architectures composed by repeaters operating through single atoms in optical cavities. Specifically, we first model the entanglement generation through a stochastic framework that allows us to jointly account for the key physical-mechanisms affecting the end-to-end entanglement rate, such as decoherence time, atom-photon and photon-photon entanglement generation, entanglement swapping, and imperfect Bell-state measurement. Then, we derive the closed-form expression of the end-to-end entanglement rate for an arbitrary path and we design an efficient algorithm for entanglement rate computation. Finally, we design a routing protocol and we prove its optimality when used in conjunction with the entanglement rate as routing metric.
In this work, we describe a routing algebra corresponding to the problem of establishing end-to-end quantum entanglements between nodes connected through a network of first generation quantum repeaters. Our goal is to design an algorithm which can determine all the routes and swapping schedules to achieve maximal rates of end-to-end entanglement. We aim to provide an improvement in terms of complexity over an existing solution while increasing the number of routes and schedules available to offer more alternatives for the entanglement generation layer of a quantum protocol stack.
This paper investigates the scalability and transmission efficiency of entanglement swapping protocols within multi-node quantum networks. As the realization of a global quantum internet relies heavily on long-distance entanglement distribution, quantum repeaters utilizing entanglement swapping serve as a critical backbone. However, scalability remains a bottleneck due to photon loss, operational infidelities, and quantum memory coherence times. In this study, we analytically model a multi-node quantum chain and evaluate how the end-to-end entanglement fidelity degrades as the number of intermediate nodes scales up. Our analysis highlights the critical thresholds for Bell state measurement (BSM) success rates required to maintain quantum state integrity across large distances. The findings provide optimization constraints for designing scalable and fault-tolerant routing protocols in future quantum information networks.
We evaluate the performance of two-way quantum repeater chains with sequential entanglement swapping. Within the analysis we consider memory decoherence, gate imperfections, and imperfect link-level entanglement generation. Our main results include closed-form expressions for the average entanglement fidelity of the generated end-to-end entangled states. We generalize previous findings for the one-shot fidelity analysis and study the case where repeater chains serve end-to-end requests continuously. We provide solutions to the continuous request scenario by combining results from quantum information theory and queuing theory. Finally, we apply the formulas obtained to analyze the impacts of hardware parameters, i.e., coherence times and gate fidelity, and distance on the entanglement fidelity and secret key rate of homogeneous quantum repeater chains.
With the emergence of the Quantum Internet, the need for advanced quantum networking techniques has significantly risen. Various models of quantum repeaters have been presented, each delineating a unique strategy to ensure quantum communication over long distances. We focus on repeaters that employ entanglement generation and swapping. This revolves around establishing remote end-to-end entanglement through repeaters, a concept we denote as the “quantum-native” repeaters (also called “first-generation” repeaters in some literature). The challenges in routing with quantum-native repeaters arise from probabilistic entanglement generation and restricted coherence time. Current approaches use synchronized time slots to search for entanglement-swapping paths, resulting in inefficiencies. Here, we propose a new set of asynchronous routing protocols for quantum networks by incorporating the idea of maintaining a dynamic topology in a distributed manner, which has been extensively studied in classical routing for lossy networks, such as using a destination-oriented directed acyclic graph or a spanning tree. The protocols update the entanglement-link topology asynchronously, identify optimal entanglement-swapping paths, and preserve unused direct-link entanglements. Our results indicate that asynchronous protocols achieve a larger upper bound with an appropriate setting and significantly higher entanglement rate than existing synchronous approaches, and the rate increases with coherence time, suggesting that it will have a much more profound impact on quantum networks as technology advances.
We consider quantum and private communications assisted by repeaters, from the basic scenario of a single repeater chain to the general case of an arbitrarily-complex quantum network, where systems may be routed through single or multiple paths. In this context, we investigate the ultimate rates at which two end-parties may transmit quantum information, distribute entanglement, or generate secret keys. These end-to-end capacities are defined by optimizing over the most general adaptive protocols that are allowed by quantum mechanics. Combining techniques from quantum information and classical network theory, we derive single-letter upper bounds for the end-to-end capacities in repeater chains and quantum networks connected by arbitrary quantum channels, establishing exact formulas under basic decoherence models, including bosonic lossy channels, quantum-limited amplifiers, dephasing and erasure channels. For the converse part, we adopt a teleportation-inspired simulation of a quantum network which leads to upper bounds in terms of the relative entropy of entanglement. For the lower bounds we combine point-to-point quantum protocols with classical network algorithms. Depending on the type of routing (single or multiple), optimal strategies corresponds to finding the widest path or the maximum flow in the quantum network. Our theory can also be extended to simultaneous quantum communication between multiple senders and receivers.