Abstract Quantum entanglement and nonlocality are foundational to quantum technologies, driving quantum computation, communication, and cryptography innovations. To benchmark the capabilities of these quantum techniques, efficient detection and accurate quantification methods are indispensable. This paper examines the concept ‘detection length’—a metric that quantifies the minimum number of simultaneously measured particles required to detect entanglement or nonlocality. We extend the detection length framework to encompass various entanglement categories and nonlocality phenomena, providing a comprehensive analytical model to determine detection lengths for specified forms of entanglement. Furthermore, we exploit semidefinite programming techniques to design entanglement witnesses and Bell’s inequalities tailored to specific minimal detection lengths, offering an upper bound for detection lengths in given states. By assessing the noise robustness of these witnesses, we demonstrate that witnesses with shorter detection lengths can exhibit superior performance under certain conditions.
Abstract Quantum entanglement and nonlocality are foundational to quantum technologies, driving quantum computation, communication, and cryptography innovations. To benchmark the capabilities of these quantum techniques, efficient detection and accurate quantification methods are indispensable. This paper examines the concept ‘detection length’—a metric that quantifies the minimum number of simultaneously measured particles required to detect entanglement or nonlocality. We extend the detection length framework to encompass various entanglement categories and nonlocality phenomena, providing a comprehensive analytical model to determine detection lengths for specified forms of entanglement. Furthermore, we exploit semidefinite programming techniques to design entanglement witnesses and Bell’s inequalities tailored to specific minimal detection lengths, offering an upper bound for detection lengths in given states. By assessing the noise robustness of these witnesses, we demonstrate that witnesses with shorter detection lengths can exhibit superior performance under certain conditions.
Multipartite entanglement is a valuable resource for quantum technologies. However, detecting this resource can be challenging: for genuine multipartite entanglement, the detection may require global measurements that are hard to implement experimentally. Here we introduce the concept of entanglement detection length, defined as the minimum number of particles that have to be jointly measured in order to detect genuine multipartite entanglement. For symmetric states, we show that the entanglement detection length can be determined by testing separability of the marginal states. For general states, we provide an upper bound on the entanglement detection length based on semidefinite programming. We show that the entanglement detection length is generally smaller than the minimum observable length needed to uniquely determine a multipartite state, and we provide examples achieving the maximum gap between these two quantities.
Multipartite entanglement is a valuable resource for quantum technologies. However, detecting this resource can be challenging: for genuine multipartite entanglement, the detection may require global measurements that are hard to implement experimentally. Here we introduce the concept of entanglement detection length, defined as the minimum number of particles that have to be jointly measured in order to detect genuine multipartite entanglement. For symmetric states, we show that the entanglement detection length can be determined by testing separability of the marginal states. For general states, we provide an upper bound on the entanglement detection length based on semidefinite programming. We show that the entanglement detection length is generally smaller than the minimum observable length needed to uniquely determine a multipartite state, and we provide examples achieving the maximum gap between these two quantities.
We propose an innovative method to enhance the detection and protection of quantum entanglement, a cornerstone of quantum mechanics with applications in computing, communication, and beyond. While entanglement can be represented through nonlocal correlations detectable by the Clauser-Horne-Shimony-Holt (CHSH) inequality, this method does not fully capture all entangled states. To address this limitation, we introduce a variational entanglement witness (VEW) that optimizes the probabilities of detection and improves the efficiency of distinguishing between separable and entangled states. Additionally, we propose a nonlocal measurement framework that enables the assessment of both CHSH inequalities and the VEW while preserving the entanglement. Our approach enhances the reliability of entanglement detection while maintaining the entanglement of quantum states, offering significant advancements for quantum technologies.
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 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.
Abstract Bell inequalities have long been essential for the device-independent detection of entanglement. This study introduces subcorrelation Bell inequalities as a robust framework for detecting entanglement and probing quantum non-locality. We derived a family of such inequalities, categorized according to their dependence on measurement settings, and numerically identified 19 distinct quantum states that achieve the maximal violation of these inequalities. Importantly, our focus on maximal violation is not for its own sake but because, in this framework, maximal violation directly corresponds to maximal robustness of nonlocal correlations against particle loss. This connection reveals a broad class of multipartite entangled states that remain resilient under loss, making them highly relevant for practical implementations of quantum information protocols. We further characterized their entanglement properties using concurrence and the geometric measure, confirming their utility for critical areas such as quantum communication, cryptography, and device-independent protocols. The framework established herein sets the stage for future investigations, including the generalization of these inequalities to higher-dimensional systems and a more comprehensive characterization of their robustness against various forms of noise, thereby expanding the potential for non-local states to drive progress in quantum technologies.