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Article

Non-Gaussianity of Four-Photon Superpositions of Fock States

1
Institute of Physics, University of Brasilia, P.O. Box 04455, Brasilia 70919-970, Brazil
2
International Center for Physics, University of Brasilia, Brasilia 70919-970, Brazil
*
Author to whom correspondence should be addressed.
Academic Editor: Yong Siah Teo
Quantum Rep. 2021, 3(3), 350-365; https://doi.org/10.3390/quantum3030022
Received: 12 June 2021 / Revised: 23 June 2021 / Accepted: 28 June 2021 / Published: 1 July 2021
(This article belongs to the Special Issue Recent Advances in Quantum Optics 2021)
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. View Full-Text
Keywords: four-photon superpositions; even vacuum squeezed states; orthogonal-even coherent states; kurtosis; Wigner function four-photon superpositions; even vacuum squeezed states; orthogonal-even coherent states; kurtosis; Wigner function
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MDPI and ACS Style

de Freitas, M.C.; Dodonov, V.V. Non-Gaussianity of Four-Photon Superpositions of Fock States. Quantum Rep. 2021, 3, 350-365. https://doi.org/10.3390/quantum3030022

AMA Style

de Freitas MC, Dodonov VV. Non-Gaussianity of Four-Photon Superpositions of Fock States. Quantum Reports. 2021; 3(3):350-365. https://doi.org/10.3390/quantum3030022

Chicago/Turabian Style

de Freitas, Miguel C., and Viktor V. Dodonov 2021. "Non-Gaussianity of Four-Photon Superpositions of Fock States" Quantum Reports 3, no. 3: 350-365. https://doi.org/10.3390/quantum3030022

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