Efficient non-Gaussianity measure for single-mode fields by kurtosis of a Gaussian operator

Abstract

We propose a method to faithfully probe and quantify the non-Gaussianity of single-mode fields in the coherent-state representations based on the averaged-cumulant technique. In comparison with the previous measure, S H Xiang et al (2018 Phys. Rev. A 97 042303), we characterize the non-Gaussianity of quantum states using the kurtosis of a Gaussian operator, rather than that of a quadrature operator. As applications, we investigate the non-Gaussianities of three different non-Gaussian states: a mixture of vacuum and Fock states, Schrödinger cat states, and photon-added coherent states. It is proven that such a kurtosis is a powerful and effective measure in appraising non-Gaussianity.

Detecting non-Gaussianity via nonclassicality

“…Resource-theoretic frameworks are proposed in [22][23][24]. Kurtosis is employed to quantifying non-Gaussianity in [25].…”

Non-Gaussianity detection of single-mode rotationally symmetric quantum states via cumulant method

“…Its fourth-order cumulant is calculated to be κ 4 = − 3 2 ng(2ng + 1 − n). [20] One sees that the κ 4 may equal zero for the case of g = n−1 2n . However, in this case, its Wigner function clearly shows negative values around the origin, i.e., non-Gaussian behaviors.…”

“…In particular, we have exploited the averaged-cumulant technique to reveal the non-Gaussianity of some typical quantum states. [16][17][18][19][20] Unfortunately, we encountered a failure of detecting the non-Gaussian natures of some quantum states using only a single higherorder cumulant. A typical case is a mixture of vacuum and n photon states of the form ρ = (1 − g)|0 0| + g|n n| with |n being a Fock state for n photons and the fractions g ∈ [0, 1].…”