This article is cited in 4 papers

Quantifying non-Gaussianity via the Hellinger distance

Yue Zhang^ab, Shunlong Luo<sup>ab

a</sup> Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, China
^b School of Mathematical Sciences, University of the Chinese Academy of Sciences, Beijing, China

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).

Keywords: bosonic field, Gaussian state, non-Gaussianity, Hellinger distance, Bures distance.

PACS: 03.65.Ta, 03.67.-a, 42.50.Dv

Received: 02.03.2020
Revised: 19.03.2020

DOI: 10.4213/tmf9895

 English version: Theoretical and Mathematical Physics, 2020, 204:2, 1046–1058

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