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arXiv:2005.07247 · npj Quantum Information

Entanglement generation in a quantum network at distance-independent rate

Ashlesha Patil, Mihir Pant, Dirk Englund, Don Towsley, Saikat Guha

Published May 6, 2022• 59 citations
arXivHTMLPDF

Abstract

Abstract We develop a protocol for entanglement generation in the quantum internet that allows a repeater node to use n-qubit Greenberger-Horne-Zeilinger (GHZ) projective measurements that can fuse n successfully-entangled links, i.e., two-qubit entangled Bell pairs shared across n network edges, incident at that node. Implementing n-fusion, for n≥3, is in principle not much harder than 2-fusions (Bell-basis measurements) in solid-state qubit memories. If we allow even 3-fusions at the nodes, we find---by developing a connection to a modified version of the site-bond percolation problem---that despite lossy (hence probabilistic) link-level entanglement generation, and probabilistic success of the fusion measurements at nodes, one can generate entanglement between end parties Alice and Bob at a rate that stays constant as the distance between them increases. We prove that this powerful network property is not possible to attain with any quantum networking protocol built with Bell measurements and multiplexing alone. We also design a two-party quantum key distribution protocol that converts the entangled states shared between two nodes into a shared secret, at a key generation rate that is independent of the distance between the two parties.

DOI
10.1038/s41534-022-00536-0

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Abstract We develop a protocol for entanglement generation in the quantum internet that allows a repeater node to use n-qubit Greenberger-Horne-Zeilinger (GHZ) projective measurements that can fuse n successfully-entangled links, i.e., two-qubit entangled Bell pairs shared across n network edges, incident at that node. Implementing n-fusion, for n≥3, is in principle not much harder than 2-fusions (Bell-basis measurements) in solid-state qubit memories. If we allow even 3-fusions at the nodes, we find---by developing a connection to a modified version of the site-bond percolation problem---that despite lossy (hence probabilistic) link-level entanglement generation, and probabilistic success of the fusion measurements at nodes, one can generate entanglement between end parties Alice and Bob at a rate that stays constant as the distance between them increases. We prove that this powerful network property is not possible to attain with any quantum networking protocol built with Bell measurements and multiplexing alone. We also design a two-party quantum key distribution protocol that converts the entangled states shared between two nodes into a shared secret, at a key generation rate that is independent of the distance between the two parties.
In a quantum network that successfully creates links—shared Bell states between neighboring repeater nodes—with probability p in each time slot, and performs Bell State Measurements at nodes with success probability q < 1, the end-to-end entanglement generation rate drops exponentially with the distance between consumers, despite multi-path routing. If repeaters can perform multi-qubit projective measurements in the GHZ basis that succeed with probability q, the rate does not change with distance in a certain (p,q) region, but decays exponentially outside. This region where the distance-independent rate occurs is the super-critical region of a new percolation problem. We extend this GHZ protocol to incorporate a time-multiplexing blocklength k, the number of time slots over which a repeater can mix-and-match successful links to perform fusion on. As k increases, the super-critical region expands. For a given (p,q), the entanglement rate initially increases with k, and once inside the super-critical region for a high enough k, it decays as 1/k GHZ states per time slot. When memory coherence time exponentially distributed with mean μ is incorporated, it is seen that increasing k does not indefinitely increase the super-critical region; it has a hard μ-dependent limit. Finally, we find that incorporating space-division multiplexing, i.e., running the above protocol independently in up to d disconnected network regions, where d is the network’s node degree, one can go beyond the 1 GHZ state per time slot rate that the above randomized local-link-state protocol cannot surpass. As (p,q) increases, one can approach the ultimate min-cut entanglement-generation capacity of d GHZ states per slot.
We study entanglement generation in a quantum network where repeater nodes can perform n-qubit Greenberger-Horne-Zeilinger(GHZ) swaps, i.e., projective measurements, to fusennnimperfect-Fidelity entangled-state fragments. We show that the distance-independent entanglement distribution rate found previously for this protocol, assuming perfectly-entangled states at the link level, does not survive. This is true also in the modified protocol we study - one that spatially constrains the repeater nodes involved in the swaps. We obtain analytical formulas for a GHZ swap of multiple Werner states, which might be of independent interest. Whether the distance-independent entanglement rate might re-emerge with a spatio-temporally-optimized scheduling of GHZ swaps and multi-site block-distillation codes, remains open.
We study entanglement generation in a quantum network where repeater nodes can perform nnn-qubit Greenberger-Horne-Zeilinger(GHZ) swaps, i.e., projective measurements, to fuse nnn imperfect-Fidelity entangled-state fragments. We show that the distance-independent entanglement distribution rate found previously for this protocol, assuming perfectly-entangled states at the link level, does not survive. This is true also in two modified protocols we study: one that incorporates l→1l \to 1l→1 link-level distillation and another that spatially constrains the repeater nodes involved in the swaps. We obtain analytical formulas for a GHZ swap of multiple Werner states, which might be of independent interest. Whether the distance-independent entanglement rate might re-emerge with a spatio-temporally-optimized scheduling of GHZ swaps and multi-site block-distillation codes remains open.
Generating a long-distance quantum entanglement is one of the most essential functions of a quantum network to support quantum communication and computing applications. The successful entanglement rate during a probabilistic entanglement process decreases dramatically with distance, and swapping is a widely-applied quantum technique to address this issue. Most existing entanglement routing protocols use a classic entanglement-swapping method based on Bell State measurements that can only fuse two successful entanglement links. This paper appeals to a more general and efficient swapping method, namely n-fusion based on Greenberger-Horne-Zeilinger measurements that can fuse n successful entanglement links, to maximize the entanglement rate for multiple quantum-user pairs over a quantum network. We propose efficient entanglement routing algorithms that utilize the properties of n-fusion for quantum networks with general topologies. Evaluation results highlight that our proposed algorithm under n-fusion can greatly improve the network performance compared with existing ones.
Abstract Remote quantum entanglement can enable numerous applications including distributed quantum computation, secure communication, and precision sensing. We consider how a quantum network—nodes equipped with limited quantum processing capabilities connected via lossy optical links—can distribute high-rate entanglement simultaneously between multiple pairs of users. We develop protocols for such quantum “repeater” nodes, which enable a pair of users to achieve large gains in entanglement rates over using a linear chain of quantum repeaters, by exploiting the diversity of multiple paths in the network. Additionally, we develop repeater protocols that enable multiple user pairs to generate entanglement simultaneously at rates that can far exceed what is possible with repeaters time sharing among assisting individual entanglement flows. Our results suggest that the early-stage development of quantum memories with short coherence times and implementations of probabilistic Bell-state measurements can have a much more profound impact on quantum networks than may be apparent from analyzing linear repeater chains. This framework should spur the development of a general quantum network theory, bringing together quantum memory physics, quantum information theory, quantum error correction, and computer network theory.
Quantum Internet has the potential to support a wide range of applications in quantum communication and quantum computing by generating, distributing, and processing quantum information. Generating a long-distance quantum entanglement is one of the most essential functions of a quantum Internet to facilitate these applications. However, entanglement is a probabilistic process, and its success rate drops significantly as distance increases. Entanglement swapping is an efficient technique used to address this challenge. How to efficiently manage the entanglement through swapping is a fundamental yet challenging problem. In this paper, we will consider two swapping methods: (1) BSM: a classic entanglement-swapping method based on Bell State measurements that fuse two successful quantum links, (2) nfusion: a more general and efficient swapping method based on Greenberger-Horne-Zeilinger measurements, capable of fusing n successful quantum links. Our goal is to maximize the entanglement rate for multiple quantum-user pairs over the quantum Internet with an arbitrary topology. We propose efficient entanglement management algorithms that utilized the unique properties of BSM and n-fusion. Evaluation results highlight that our approach outperforms existing routing protocols.