# Entanglement Certification $-$ From Theory to Experiment

## TL;DR

This paper reviews methods for detecting and certifying quantum entanglement in experiments, emphasizing practical approaches, assumptions, and the challenges of quantification across various quantum systems.

## Contribution

It provides a comprehensive survey of entanglement detection and certification techniques, highlighting their theoretical foundations and experimental implementations.

## Key findings

- Various entanglement quantifiers and classifiers are discussed.
- Survey of state-of-the-art detection methods and their assumptions.
- Analysis of the resource efficiency and applicability of different approaches.

## Abstract

Entanglement is an important resource that allows quantum technologies to go beyond the classically possible. There are many ways quantum systems can be entangled, ranging from the archetypal two-qubit case to more exotic scenarios of entanglement in high dimensions or between many parties. Consequently, a plethora of 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. This is further exacerbated by the difficulty of experimentally controlling and measuring complex quantum states. Consequently, there are various approaches for experimentally detecting and certifying entanglement when exact quantification is not an option, with a particular focus on practically implementable methods and resource efficiency. The applicability and performance of these methods strongly depends on the assumptions one is willing to make 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 paradigmatic quantifiers of entanglement. For these, we survey state-of-the-art detection and certification methods, including their respective underlying assumptions, from both a theoretical and experimental point of view.