Entanglement Detection and Certification
The problem of certifying quantum systems is not limited to technology available now or in the near future, but is tied to a fundamental question regarding the application of the scientific method to highcomplexity quantum systems: How can one hope to test the quantummechanical predictions for devices whose complexity (as captured by the statespace dimension) increases exponentially with the number of their constituents, when one can only use classical computers to check? As put by Aharonov and Vazirani [pp. 2 in arXiv:1206.3686], “...rather than predicting the actual outcome of the experiment, what is predicted is that the outcome passes a test specified by a certain computational process...". This leads to the question: What can be considered a convincing and feasibly implementable test of this kind, demonstrating the functionality of quantum devices in the NISQera and beyond?
Although a number of different benchmarking tasks have been developed to test the functionality of quantum technologies, full characterization is often too demanding or not efficiently possible even for NISQera devices. However, a common trait (although not necessarily the raison d’ ˆ etre) of many quantum technologies is the (expected) ability to generate and maintain complex structures of genuine quantum correlations, i.e., entanglement. Entanglement certification thus represents a class of tests in the spirit of Aharonov and Vazirani. This is a feature that I aim to exploit in my research and for which I hope to deliver novel solutions: Detection and certification of bipartite entanglement and nonclassicality (Bellinequality violation) across (all) qubit connections, or of genuine multipartite entanglement (GME) and highdimensional entanglement (HDE) can serve as benchmarks. Experimental confirmation of the presence of entanglement implies appropriate levels of coherence (and hence the quantumnature of the system) and the ability to fully control the system, providing a practical check for proper connectivity and coherence in complex localized systems (e.g., a quantum simulator). A working hypothesis is that the certification of entanglement structures can be further used to characterize the structure of underlying devices and quantum dynamics and even quantum networks.

Below you can find a list of recent projects and ideas I have been pursuing in this research area, for a review on the state of the art as well as current challenges in entanglement detection can be found in our review [Nicolai Friis, Giuseppe Vitagliano, Mehul Malik, and Marcus Huber, Entanglement certification from theory to experiment, Nat. Rev. Phys. 1, 72 (2019), arXiv:1906.10929].