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.
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.
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 the premier resource for quantum technologies. Yet, its exact quantification in the laboratory is notoriously challenging, typically requiring the full knowledge of high dimensional quantum states. Here, we construct observable bounds to multipartite entanglement for systems of arbitrary size, which are functions of the local and global state purities, and correlation functions. First, we derive experimentally accessible upper and lower limits to both the bipartite entanglement of formation and the squashed entanglement of bipartite systems, by leveraging cornerstone results of quantum information theory: the entropy strong subadditivity inequality and the Koashi-Winter monogamy relation. Then, we convert them into bounds to the entanglement up to degree k for arbitrary states, and to the genuine k-partite entanglement, by employing a recently proposed method. Finally, we analytically and numerically test these results, by bounding the multipartite entanglement of several relevant states and mixtures, including the important classes of GHZ, Dicke, W states, and random pure states.
Genuine multipartite entanglement (GME) is a valuable resource for quantum technologies, but quantifying it in many-body systems can be demanding since measures defined through optimizations over bipartitions are often assumed to require large joint measurements and many measurement settings. We introduce the concepts of GME evaluation length and GME evaluation number, which capture, respectively, the largest subsystem that must be jointly measured and the number of distinct subsystems that need to be measured to evaluate multipartite entanglement measures defined via bipartition optimizations. Taking the genuine multipartite concurrence (GMC) as a canonical example, we show that, for N-qubit Haar-random pure states, the GMC can be evaluated using only N single-qubit purity measurements. Thus, for typical many-body states, evaluating the GMC requires considering only the N single-site bipartitions, rather than the exponentially many distinct bipartitions. We further corroborate this behavior numerically for physically accessible states generated by local random quantum circuits. Our results show that the practical cost of quantifying GME can be dramatically lower than suggested by its formal definition, establishing measurement complexity as a complementary operational lens for multipartite entanglement.
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.