Developing improved measures of non-Gaussianity and Gaussianity for quantum states based on normalized Hilbert–Schmidt distance

• Published in: Chinese physics B 2023-05, Vol.32 (5), p.50309-343
• Main Authors: Xiang, Shaohua, Li, Shanshan, Mi, Xianwu
• Format: Article
• Language: English
• Subjects: non-Gaussian states; non-Gaussianity measure; phase-space distribution function
• ISSN: 1674-1056
• DOI: 10.1088/1674-1056/acb0bd

Non-Gaussianity of quantum states is a very important source for quantum information technology and can be quantified by using the known squared Hilbert–Schmidt distance recently introduced by Genoni et al. ( Phys. Rev. A 78 042327 (2007)). It is, however, shown that such a measure has many imperfects such as the lack of the swapping symmetry and the ineffectiveness evaluation of even Schrödinger-cat-like states with small amplitudes. To deal with these difficulties, we propose an improved measure of non-Gaussianity for quantum states and discuss its properties in detail. We then exploit this improved measure to evaluate the non-Gaussianities of some relevant single-mode non-Gaussian states and multi-mode non-Gaussian entangled states. These results show that our measure is reliable. We also introduce a modified measure for Gaussianity following Mandilara and Cerf ( Phys. Rev. A 86 030102(R) (2012)) and establish a conservation relation of non-Gaussianity and Gaussianity of a quantum state.