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Creating large-scale entanglement lies at the heart of many quantuminformation processing protocols and the investigation of fundamental physics.For multipartite quantum systems, it is crucial to identify not only thepresence of entanglement but also its detailed structure. This is because in ageneric experimental situation with sufficiently many subsystems involved, theproduction of so-called genuine multipartite entanglement remains a formidablechallenge. Consequently, focusing exclusively on the identification of thisstrongest type of entanglement may result in an all or nothing situation wheresome inherently quantum aspects of the resource are overlooked. On thecontrary, even if the system is not genuinely multipartite entangled, there maystill be many-body entanglement present in the system. An identification of theentanglement structure may thus provide us with a hint about whereimperfections in the setup may occur, as well as where we can identify groupsof subsystems that can still exhibit strong quantum-information-processingcapabilities. However, there is no known efficient methods to identify theunderlying entanglement structure. Here, we propose two complementary familiesof witnesses for the identification of such structures. They are based on thedetection of entanglement intactness and entanglement depth, each requires onlythe implementation of solely two local measurements. Our method is also robustagainst noises and other imperfections, as reflected by our experimentalimplementation of these tools to verify the entanglement structure of fivedifferent eight-photon entangled states. We demonstrate how their entanglementstructure can be precisely and systematically inferred from the experimentaldata. In achieving this goal, we also illustrate how the same set of data canbe classically postprocessed to learn the most about the measured system.

Entanglement Structure: Entanglement Partitioning in Multipartite Systems and Its Experimental Detection Using Optimizable Witnesses