Abstract
We study two families of four-photon superpositions of the Fock states: even vacuum squeezed states (EVSS) and orthogonal-even coherent states (OECS). These families are distinguished due to several properties: for certain values of parameters, they give the fourth-order uncertainty products close to the known minimal value (which is lower than for the Gaussian states); they have equal dimensionless values of the second- and fouth-order moments of the coordinate and momentum for all values of parameters; they possess zero covariances for all values of parameters. Since these states are obviously non-Gaussian, we consider them as good candidates to compare several different measures of non-Gaussianity proposed by different authors for the past fifteen years. The reference Gaussian states in all examples are thermal states dependent on a single parameter (an effective temperature or the coordinate variance). We analyze the measures based on the normalized Hilbert–Schmidt distance and the relative entropy (introduced by Genoni–Paris–Banaszek), the fidelity measure (Ghiu–Marian–Marian) and its logarithmic analog (Baek–Nha), as well as the Mandilara–Karpov–Cerf “Gaussianity parameter”. These measures are compared with the kurtosis of the coordinate probability density and with the non-Gaussian behavior of the Wigner function.
Highlights
Non–Gaussian states play an important role in quantum optics
For pure quantum states considered in this paper, other non-Gaussianity measures can be written in terms of T and σ as follows: δT
It is difficult to choose any of these measures as the “best” one: all of them seem more or less equivalent, at least for the pure quantum states studied in this paper
Summary
Non–Gaussian states play an important role in quantum optics. It is enough to remember that the basic Fock states are strongly non-Gaussian. Where the second equality holds for any pure state ρ = |ψ ψ| Following this line of reasoning, the authors of paper [7] introduced the following measure of non-Gaussianity: Tr (ρ − ρG) δT[ρ] = 2Tr(ρ2). Quantum Rep. 2021, 3 generalizations to the case of mixed quantum states were made on the basis of the so-called Wigner–Yanase skew information [60] Another idea is to replace zero in the right-hand side of Equation (9) with some function containing some measure of non-Gaussianity. The second family of states, considered, consists of superpositions of four coherent states with equal amplitudes, but with phases shifted by π/2: These kinds of states were studied for a long time from different points of view. Following [71], we use the abbreviation OECS for the state Equation (15)
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
