Alternative non-Gaussianity measures for quantum states based on quantum fidelity |
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| Affiliation: | 1.College of Electrical and Information Engineering, Huaihua University, Huaihua 418008, China;2.Hunan Provincial Key Laboratory of Ecological Agriculture Intelligent Control Technology, Huaihua 418008, China |
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| Abstract: | We propose three alternative measures for non-Gaussianity of quantum states: sine distance, Bures angle, and Bures distance, which are based on quantum fidelity introduced by Wang Phys. Lett. A 373 58 (2008)]. Using them, we evaluate the non-Gaussianity of some relevant single-mode and two-mode non-Gaussian states and find a good consistency of the three examined measures. In addition, we show that such metrics can exactly quantify the degree of Gaussianity of even Schrödinger-cat-like states of small amplitudes that can not be measured by other known non-Gaussianity measures such as the Hilbert—Schmidt metric and the relative entropy metric. We make a comparative study between all existing non-Gaussianity measures according to the metric axioms and point out that the sine distance is the best candidate among them. |
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| Keywords: | non-Gaussianity quantum fidelity non-Gaussian states sine metric |
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