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

Abstract

Creating large-scale entanglement lies at the heart of many quantum information processing protocols and the investigation of fundamental physics. For multipartite quantum systems, it is crucial to identify not only the presence of entanglement but also its detailed structure. This is because in a generic experimental situation with sufficiently many subsystems involved, the production of so-called genuine multipartite entanglement remains a formidable challenge. Consequently, focusing exclusively on the identification of this strongest type of entanglement may result in an all or nothing situation where some inherently quantum aspects of the resource are overlooked. On the contrary, even if the system is not genuinely multipartite entangled, there may still be many-body entanglement present in the system. An identification of the entanglement structure may thus provide us with a hint about where imperfections in the setup may occur, as well as where we can identify groups of subsystems that can still exhibit strong quantum-information-processing capabilities. However, there is no known efficient methods to identify the underlying entanglement structure. Here, we propose two complementary families of witnesses for the identification of such structures. They are based, respectively, on the detection of entanglement intactness and entanglement depth, each applicable to an arbitrary number of subsystems and whose evaluation requires only the implementation of solely two local measurements. Our method is also robust against noises and other imperfections, as reflected by our experimental implementation of these tools to verify the entanglement structure of five different eight-photon entangled states. In particular, we demonstrate how their entanglement structure can be precisely and systematically inferred from the experimental measurement of these witnesses. In achieving this goal, we also illustrate how the same set of data can be classically postprocessed to learn the most about the measured system.

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Plain Language Summary

Quantum entanglement is of paramount importance not only to our understanding of nature but also to the implementation of quantum information processing tasks. While many experiments attempt to create large-scale entanglement among hundreds of atoms, they instead end up with a mixture of groups containing much fewer entangled atoms. The ability to precisely characterize the entanglement among all the components in a large ensemble could provide not only a useful diagnostic of where the imperfections in our devices lie but also a clear benchmark of our technological progress towards the ultimate goal of creating true large-scale entanglement. We report here a novel means of identifying entanglement that can be used for this characterization.

Our tools consist of two families of “entanglement witnesses”: One identifies the extent to which entanglement is segregated among groups of subsystems; the other characterizes the minimal number of particles that are genuinely entangled. Each of our tools can be applied to a system involving arbitrarily many subsystems. They require the measurement of only two local observables, and can further be optimized classically after the measurement is completed. These tools can generally return nontrivial information on entanglement structure. We further report a proof-of-principle experiment illustrating how our tools can be applied in a systematic manner to reveal the entanglement structure of various eight-photon entangled states.

An adaptation of our tools to quantum states that are useful for measurement-based quantum computation would help us move towards the demonstration of quantum supremacy, the potential advantage of quantum computers to solve problems that classical computers cannot.