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 high-complexity quantum systems: How can one hope to test the quantum-mechanical predictions for devices whose complexity (as captured by the state-space 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 NISQ-era 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 NISQ-era 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 non-classicality (Bell-inequality violation) across (all) qubit connections, or of genuine multipartite entanglement (GME) and high-dimensional entanglement (HDE) can serve as benchmarks. Experimental confirmation of the presence of entanglement implies appropriate levels of coherence (and hence the quantum-nature 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.
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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].