Regensburg 2022 – wissenschaftliches Programm

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QI: Fachverband Quanteninformation

QI 3: Certification and Benchmarking of Quantum Systems

QI 3.3: Vortrag

Montag, 5. September 2022, 15:45–16:00, H8

Spin squeezing inequalities meet randomized measurements — •Jan Lennart Bönsel, Satoya Imai, Ye-Chao Liu, and Otfried Gühne — University of Siegen, Siegen, Germany

Due to the recent advances in quantum control, large quantum systems containing thousands of atoms can nowadays be prepared in the lab. Here, the characterization of quantum correlations is of special interest. For systems where the individual atoms are difficult to address, the measurement of collective angular momentum observables and the evaluation of the corresponding spin squeezing inequalities are a possibility to characterize entanglement and its usefulness for metrology.

In this contribution, we first study the number of quantum state samples that are necessary to verify entanglement with a certain confidence. For this purpose, we compare different estimators of spin squeezing parameters. We characterize the probability that the estimator deviates from its mean using simulations as well as analytical bounds derived from concentration inequalities, like Cantelli's and Hoeffding's inequality. Second, we analyse if it is possible to obtain a good estimate from fewer measurements made only on a randomly chosen subset of the atoms.