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

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 imperfec...

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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
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Summary: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.
ISSN:1674-1056
DOI:10.1088/1674-1056/acb0bd