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arXiv 0812.2800quant-ph
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量子态的非高斯性度量

A measure of non-Gaussianity for quantum states

J. Solomon Ivan, M. Sanjay Kumar, R. Simon

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摘要：

提出了一种$n$振子模系统的量子态的非高斯性测度。我们的测量是基于准概率$Q(α), α\in{\cal C}^n$。由于任何非高斯性的度量都必须试图对$Q$函数的形状与高斯的偏离做出定量陈述，因此任何好的非高斯性度量在不改变$Q$函数形状的变换下都应该是不变的，即位移、通过被动线性系统和所有相空间变量的均匀缩放：$Q(α)\to λ^{2n}Q(λα)$。我们的措施，满足这个“形状标准”计算几个家庭的状态，并与现有的措施的非高斯的结果进行了对比。形状准则意味着，特别是，非高斯的光子添加的热状态应该是独立的温度。

英文摘要：

We propose a measure of non-Gaussianity for quantum states of a system of $n$ oscillator modes. Our measure is based on the quasi-probability $Q(α), α\in{\cal C}^n$. Since any measure of non-Gaussianity is necessarily an attempt at making a quantitative statement on the departure of the shape of the $Q$ function from Gaussian, any good measure of non-Gaussianity should be invariant under transformations which do not alter the shape of the $Q$ functions, namely displacements, passage through passive linear systems, and uniform scaling of all the phase space variables: $Q(α)\to λ^{2n}Q(λα)$. Our measure which meets this `shape criterion' is computed for a few families of states, and the results are contrasted with existing measures of non-Gaussianity. The shape criterion implies, in particular, that the non-Gaussianity of the photon-added thermal states should be independent of temperature.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

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