We address the quantification of non-Gaussianity of states and operations in continuous-variable systems and its use in quantum information. We start by illustrating in details the properties and the relationships of two recently proposed measures of non-Gaussianity based on the Hilbert-Schmidt (HS) distance and the quantum relative entropy (QRE) between the state under examination and a reference Gaussian state. We then evaluate the non-Gaussianities of several families of non-Gaussian quantum states and show that the two measures have the same basic properties and also share the same qualitative behaviour on most of the examples taken into account. However, we also show that they introduce a different relation of order, i.e. they are not strictly monotone each other. We exploit the non-Gaussianity measures for states in order to introduce a measure of non-Gaussianity for quantum operations, to assess Gaussification and de-Gaussification protocols, and to investigate in details the role played by non-Gaussianity in entanglement distillation protocols. Besides, we exploit the QRE-based non-Gaussianity measure to provide new insight on the extremality of Gaussian states for some entropic quantities such as conditional entropy, mutual information and the Holevo bound. We also deal with parameter estimation and present a theorem connecting the QRE nonG to the quantum Fisher information. Finally, since evaluation of the QRE nonG measure requires the knowledge of the full density matrix, we derive some {\em experimentally friendly} lower bounds to nonG for some class of states and by considering the possibility to perform on the states only certain efficient or inefficient measurements.
Fermionic non-Gaussianity via computable measures and experimentally accessible bounds
Pitaevskii BEC Center, CNR-INO and Dipartimento di Fisica, Università di Trento（庞塔夫斯基玻色-爱因斯坦凝聚中心，意大利国家研究委员会光学研究所和特伦托大学物理系）；INFN-TIFPA, Trento Institute for Fundamental Physics and Applications（INFN-TIFPA，特伦托基础物理与应用研究所）
Practical Tests and Witnesses of Fermionic non-Gaussianity
Quantum Research Center, Technology Innovation Institute（技术革新研究所量子研究中心）；Institut für Theoretische Physik, Universität zu Köln（科隆大学理论物理研究所）；Barcelona Supercomputing Center（巴塞罗那超级计算中心）
Uncovering Non-Gaussianity through Multi-Copy Symmetries
Beijing Institute of Mathematical Sciences and Applications（北京国际数学研究中心）；State Key Laboratory of Mathematical Sciences, Academy of Mathematics and Systems Science, Chinese Academy of Sciences（中国科学院数学与系统科学研究院数学科学重点实验室）；School of Mathematical Sciences, University of Chinese Academy of Sciences（中国科学院大学数学科学学院）
Classical simulation and quantum resource theory of non-Gaussian optics
Wallenberg Centre for Quantum Technology, Department of Microtechnology and Nanoscience, Chalmers University of Technology（瓦伦堡量子技术中心，微技术和纳米科学系，查尔姆斯理工大学）；Department of Basic Science, The University of Tokyo（基础科学系，东京大学）；Department of Physics, Graduate School of Science, The University of Tokyo（理学院物理系，东京大学）；Department of Computer Science, Graduate School of Information Science and Technology, The University of Tokyo（信息理工学院计算机科学系，东京大学）
Université Paris Cité（巴黎西岱大学）；CNRS（法国国家科学研究中心）；Laboratoire Matériaux et Phénomènes Quantiques（材料与量子现象实验室）；Département de Physique de l’Ecole Normale Supérieure - PSL（巴黎高等师范学院物理系-PSL）；Département de Mathématiques et Applications - PSL（数学与应用系-PSL）；Département de Physique, Université Paris-Saclay（巴黎萨克雷大学物理系）
