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arXiv:2303.17771 · npj Quantum Information

Scalable determination of multipartite entanglement in quantum networks

Wei‐Ting Kao, Chien-Ying Huang, Tung-Ju Tsai, Shih-Hsuan Chen, Sheng-Yan Sun, Yucheng Li, Teh‐Lu Liao, Chih‐Sung Chuu, He Lu, Che‐Ming Li

Published Aug 8, 2024• 6 citations
arXivHTMLPDF

Abstract

Quantum networks comprised of entangled end nodes serve stronger than the classical correlation for unparalleled quantum internet applications. However, practical quantum networking is affected by noise, which at its worst, causes end nodes to be described by pre-existing classical data. In such untrusted networks, determining quantum network fidelity and genuine multi-node entanglement becomes crucial. Here, we show that determining quantum network fidelity and genuine N -node entanglement in an untrusted star network requires only N + 1 measurement settings. This method establishes a semi-trusted framework, allowing some nodes to relax their assumptions. Our network determination method is enabled by detecting genuine N -node Einstein-Podolsky-Rosen steerability. Experimentally, using spontaneous parametric down-conversion entanglement sources, we demonstrate the determinations of genuine 3-photon and 4-photon quantum networks and the false positives of the widely used entanglement witness, the fidelity criterion of 1/2. Our results provide a scalable method for the determination of multipartite entanglement in realistic quantum networks.

DOI
10.1038/s41534-024-00867-0

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Quantum networks comprised of entangled end nodes serve stronger than the classical correlation for unparalleled quantum internet applications. However, practical quantum networking is affected by noise, which at its worst, causes end nodes to be described by pre-existing classical data. In such untrusted networks, determining quantum network fidelity and genuine multi-node entanglement becomes crucial. Here, we show that determining quantum network fidelity and genuine N -node entanglement in an untrusted star network requires only N + 1 measurement settings. This method establishes a semi-trusted framework, allowing some nodes to relax their assumptions. Our network determination method is enabled by detecting genuine N -node Einstein-Podolsky-Rosen steerability. Experimentally, using spontaneous parametric down-conversion entanglement sources, we demonstrate the determinations of genuine 3-photon and 4-photon quantum networks and the false positives of the widely used entanglement witness, the fidelity criterion of 1/2. Our results provide a scalable method for the determination of multipartite entanglement in realistic quantum networks.
Quantum networks illustrate the use of connected nodes of quantum systems as the backbone of distributed quantum information processing. When the network nodes are entangled in graph states, such a quantum platform is indispensable to almost all the existing distributed quantum tasks. Unfortunately, real networks unavoidably suffer from noise and technical restrictions, making nodes transit from quantum to classical at worst. Here, we introduce a figure of merit in terms of the number of classical nodes for quantum networks in arbitrary graph states. Such a network property is revealed by exploiting a novel Einstein-Podolsky-Rosen steerability. Experimentally, we demonstrate photonic quantum networks of n_{q} quantum nodes and n_{c} classical nodes with n_{q} up to 6 and n_{c} up to 18 using spontaneous parametric down-conversion entanglement sources. We show that the proposed method is faithful in quantifying the classical defects in prepared multiphoton quantum networks. Our results provide novel identification of generic quantum networks and nonclassical correlations in graph states.
The design of detection strategies for multipartite entanglement stands as a central importance on our understanding of fundamental quantum mechanics and has had a substantial impact on quantum information applications. However, accurate and robust detection approaches are severely hindered, particularly when the number of nodes grows rapidly like in a quantum network. Here we present a general and operational framework that generates alternative entanglement witness for an arbitrary targeted state. The framework enjoys a systematic and high-efficient character and allows to substantiate genuine multipartite entanglement for a variety of states that arise naturally in practical situations and to dramatically outperform currently standard methods. With excellent noise tolerance, our framework should be broadly applicable to witness genuine multipartite entanglement in various practically scenarios and to facilitate the best use of entangled resources in the emerging area of quantum network.
Multipartite entangled states are a fundamental resource for a wide range of quantum information processing tasks. In particular, in quantum networks, it is essential for the parties involved to be able to verify if entanglement is present before they carry out a given distributed task. Here we design and experimentally demonstrate a protocol that allows any party in a network to check if a source is distributing a genuinely multipartite entangled state, even in the presence of untrusted parties. The protocol remains secure against dishonest behaviour of the source and other parties, including the use of system imperfections to their advantage. We demonstrate the verification protocol in a three- and four-party setting using polarization-entangled photons, highlighting its potential for realistic photonic quantum communication and networking applications.
Quantum networks form the backbone of long-distance quantum information processing. Genuine multipartite entanglement (GME) serves as a key indicator of network performance and overall state quality. However, the widely used methods for certifying GME suffer from a major drawback that they either detect only a limited range of states or are applicable only to systems with a small number of parties. To overcome these limitations, we propose a family of sub-symmetric witnesses (SSWs), which are tractable both theoretically and experimentally. Analytically, we establish a connection between SSWs and the cut space of graph theory, enabling several powerful detection criteria tailored to practical quantum networks. Numerically, we show that the optimal detection can be formulated as a linear program, offering a significant efficiency advantage over the semidefinite programs commonly employed in quantum certification. Experimentally, SSWs can be evaluated via local measurements, with resource requirements independent of the local dimension in general, and even independent of the overall network size in many practical networks.
The future of quantum communication relies on quantum networks composed by observers sharing multipartite quantum states. The certification of multipartite entanglement will be crucial to the usefulness of these networks. In many real situations it is natural to assume that some observers are more trusted than others in the sense that they have more knowledge of their measurement apparatuses. Here we propose a general method to certify all kinds of multipartite entanglement in this asymmetric scenario and experimentally demonstrate it in an optical experiment. Our results, which can be seen as a definition of genuine multipartite quantum steering, give a method to detect entanglement in a scenario in between the standard entanglement and fully device-independent scenarios, and provide a basis for semi-device-independent cryptographic applications in quantum networks.
How can one detect entanglement between multiple optical paths sharing a single photon? We address this question by proposing a scalable protocol, which only uses local measurements where single photon detection is combined with small displacement operations. The resulting entanglement witness does not require postselection, nor assumptions about the photon number in each path. Furthermore, it guarantees that entanglement lies in a subspace with at most one photon per optical path and reveals genuinely multipartite entanglement. We demonstrate its scalability and resistance to loss by performing various experiments with two and three optical paths. We anticipate applications of our results for quantum network certification.