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Quantifying non-Gaussianity via the Hellinger distance

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Abstract

Non-Gaussianity is an important resource for quantum information processing with continuous variables. We introduce a measure of the non-Gaussianity of bosonic field states based on the Hellinger distance and present its basic features. This measure has some natural properties and is easy to compute. We illustrate this measure with typical examples of bosonic field states and compare it with various measures of non-Gaussianity. In particular, we highlight its similarity to and difference from the measure based on the Bures distance (or, equivalently, fidelity).

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Funding

This research was supported by the National Natural Science Foundation of China (Grant No. 11875317), the National Center for Mathematics and Interdisciplinary Sciences, Chinese Academy of Sciences (Grant No. Y029152K51), and the Key Laboratory of Random Complex Structures and Data Science, Chinese Academy of Sciences (Grant No. 2008DP173182).

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  1. Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, China

    Yue Zhang & Shunlong Luo

  2. School of Mathematical Sciences, University of the Chinese Academy of Sciences, Beijing, China

    Yue Zhang & Shunlong Luo

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  1. Yue Zhang
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Zhang, Y., Luo, S. Quantifying non-Gaussianity via the Hellinger distance. Theor Math Phys 204, 1046–1058 (2020). https://doi.org/10.1134/S0040577920080061

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