Entanglement certification from theory to experiment

Entanglement is an important resource for quantum technologies. There are many ways quantum systems can be entangled, ranging from the two-qubit case to entanglement in high dimensions or between many parties. Consequently, many entanglement quantifiers and classifiers exist, corresponding to different operational paradigms and mathematical techniques. However, for most quantum systems, exactly quantifying the amount of entanglement is extremely demanding, if at all possible. Furthermore, it is difficult to experimentally control and measure complex quantum states. Therefore, there are various approaches to experimentally detect and certify entanglement when exact quantification is not an option. The applicability and performance of these methods strongly depend on the assumptions regarding the involved quantum states and measurements, in short, on the available prior information about the quantum system. In this Review, we discuss the most commonly used quantifiers of entanglement and survey the state-of-the-art detection and certification methods, including their respective underlying assumptions, from both a theoretical and an experimental point of view.Entanglement is often considered the defining feature separating classical physics from quantum physics and provides the basis for many quantum technologies. This Review discusses recent progress in the challenging task of conclusively proving that a physical system features entanglement, surveying detection and certification methods.Key pointsEntanglement detection and certification are of high significance for ensuring the security of quantum communication, improving the sensitivity of sensing devices, and benchmarking devices for quantum computation and simulation.Recent years have seen continuous progress in the development of tools for entanglement certification and an increase in control over a wide variety of experimental setups suitable for entanglement creation.Goals for the development of entanglement detection techniques are device-independence and assumption-free certification.Current challenges include the extension of well-understood methods for two qubits to many-body and/or high-dimensional quantum systems and their application in entanglement experiments with ions, atoms and photons.An important focus of recent research is the reduction in the number of measurements required for entanglement certification to cope with increasing system dimensions.