2018/12/19 by Nicolai Friis, Giuseppe Vitagliano, Mehul Malik +1 · 17 citations
Computer Science · Physics and Astronomy · #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum Mechanics and Applications #quant-ph
paper · pdf · doi:10.1038/s42254-018-0003-5
published as Nat. Rev. Phys. 1, 72-87 (2019) · 16 pages plus references, updated version of an abridged manuscript published in Nature Reviews Physics
crossref issued 2018/12/19 · crossref published 2018/12/19 · crossref published-online 2018/12/19 · openalex publication_date 2018/12/19 · crossref created 2018/12/19 · openalex created_date 2018/12/22 · arxiv created 2019/06/26 · arxiv updated 2019/06/27 · crossref deposited 2022/12/17 · openalex updated_date 2026/07/28 · crossref indexed 2026/08/04
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.