Quantifying non-Gaussianity via the Hellinger distance
Yue Zhang, Shunlong Luo · Theoretical and Mathematical Physics · 2020
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).