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arXiv:2104.08216 · Quantum

Local and scalable detection of genuine multipartite single-photon path entanglement

Patrik Caspar, Enky Oudot, Pavel Sekatski, Nicolas Maring, Anthony Martin, Nicolas Sangouard, Hugo Zbinden, Rob Thew

Published Mar 22, 2022• 8 citations
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Abstract

How can a multipartite single-photon path-entangled state be certified efficiently by means of local measurements? We address this question by constructing an entanglement witness based on local photon detections preceded by displacement operations to reveal genuine multipartite entanglement. Our witness is defined as a sum of three observables that can be measured locally and assessed with two measurement settings for any number of parties N . For any bipartition, the maximum mean value of the witness observable over biseparable states is bounded by the maximum eigenvalue of an N×N matrix, which can be computed efficiently. We demonstrate the applicability of our scheme by experimentally testing the witness for heralded 4- and 8-partite single-photon path-entangled states. Our implementation shows the scalability of our witness and opens the door for distributing photonic multipartite entanglement in quantum networks at high rates.

DOI
10.22331/q-2022-03-22-671

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How can a multipartite single-photon path-entangled state be certified efficiently by means of local measurements? We address this question by constructing an entanglement witness based on local photon detections preceded by displacement operations to reveal genuine multipartite entanglement. Our witness is defined as a sum of three observables that can be measured locally and assessed with two measurement settings for any number of parties N . For any bipartition, the maximum mean value of the witness observable over biseparable states is bounded by the maximum eigenvalue of an N×N matrix, which can be computed efficiently. We demonstrate the applicability of our scheme by experimentally testing the witness for heralded 4- and 8-partite single-photon path-entangled states. Our implementation shows the scalability of our witness and opens the door for distributing photonic multipartite entanglement in quantum networks at high rates.
Multipartite entanglement is a key resource for quantum technologies, yet its certification typically relies on correlations from measurements involving all particles, making it increasingly vulnerable to imperfections as the system size grows. Here we report the first experimental demonstration of genuine multipartite entanglement detection from correlations with the minimum possible nontrivial support, known as the entanglement detection length (EDL). Using a photonic platform, we certify W, Dicke, and cluster states with entanglement witnesses constructed from correlations at the EDL. In particular, we verify genuine multipartite entanglement of three- and four-qubit W states and a four-qubit Dicke state using two-body correlations, and of a four-qubit cluster state using three-body correlations. For the four-photon Dicke state, we further show that this minimal-correlation strategy is more robust than the compared global witness under the analyzed local-basis-misalignment model. We also find that, within the witness families considered here, increasing the number of measured subsets enhances the tolerance to noise. These results establish entanglement detection at the EDL limit as a measurement-efficient route to multipartite entanglement certification.
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.
Multipartite entanglement plays a critical role in various applications of quantum internet. In these applications, the entanglement is usually shared by the distant parties. Experimentally, the distributed entanglement should be estimated by only local measurements. Furthermore, for network experiments, it is desirable to employ measurement techniques that are straightforward to implement. In this paper, we propose a method to measure arbitrary multipartite single-photon path entangled states by only local measurements. By considering practically reasonable assumptions, our method is relatively easy to implement. We experimentally demonstrate the utility of this method by reconstructing the density matrix of a 3-qubit W state.
Certifying genuine multipartite entanglement in quantum systems can require a number of measurements that grows exponentially with the system size. Here we introduce a criterion based on correlation-tensor subsector lengths restricted to local measurement planes and show that it can be evaluated using partially randomized measurements without an explicit exponential dependence on the number of qubits. We derive the corresponding bounds for kkk-separable states and illustrate the criterion using representative families of multipartite entangled states. Finally, we demonstrate the practical applicability of the method on an ion-trap quantum computer by certifying genuine five-partite entanglement.
Standard procedures for entanglement detection assume that experimenters can exactly implement specific quantum measurements. Here, we depart from such idealizations and investigate, in both theory and experiment, the detection of genuine multipartite entanglement when measurements are subject to small imperfections. For arbitrary qubits number n, we construct multipartite entanglement witnesses where the detrimental influence of the imperfection is independent of n. In a tabletop four-partite photonic experiment, we demonstrate first how a small amount of alignment error can undermine the conclusions drawn from standard entanglement witnesses and then perform the correction analysis. Furthermore, since we consider quantum devices that are trusted but not perfectly controlled, we showcase advantages in terms of noise resilience as compared to device-independent models.
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.