# Non-Gaussianity of Four-Photon Superpositions of Fock States

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## Abstract

**:**

## 1. Introduction

## 2. Non-Gaussianity of Arbitrary Four-Photon Superpositions and Mixtures

## 3. Non-Gaussianity Measures in EVSS

## 4. Non-Gaussianity Measures in OECS

## 5. Comparison of Non-Gaussianity of EVSS and OECS

## 6. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**The probability density Equation (34) of EVSS for different values of the squeezing parameter r.

**Left**: $\theta =\pi /2$.

**Right**: $\theta =0$.

**Figure 2.**The section ${W}_{z}(q,0)$ of EVSS for different values of the squeezing parameter r and phase $\theta $.

**Left**: $\theta =0$; $r=0,1.0,2.0$.

**Right**: $\theta =\pi /2$, the same values of r.

**Figure 3.**The behavior of the non-Gaussianity measures (

**left**) and kurtosis (

**right**) as functions of parameters c and r, respectively, for the Even Vacuum Squeezed States.

**Figure 4.**Real wave functions of OECS for different values of parameter $\alpha =\sqrt{a}exp\left(i\varphi \right)$.

**Left**: $\varphi =0$.

**Right**: $\varphi =\pi /4$.

**Figure 5.**The coordinate probability density of OECS for different values of parameter $a={\left|\alpha \right|}^{2}$ and phase $\varphi $.

**Left**: $\varphi =0$.

**Right**: $\varphi =\pi /4$.

**Figure 6.**The sections of function ${W}_{4\alpha}(q,p)$ for different values of real parameter $\alpha =\sqrt{a}$.

**Left**: ${W}_{4\alpha}(q,0)$.

**Right**: ${W}_{4\alpha}(q,q)$.

**Figure 7.**The sections of function ${W}_{4\alpha}(q,p)$ for $\alpha =\left|\alpha \right|exp(i\pi /4)$.

**Left**: ${W}_{4\alpha}(q,0)$.

**Right**: ${W}_{4\alpha}(q,q)$.

**Figure 8.**The behavior of the non-Gaussianity measures (

**left**) and kurtosis (

**right**) as functions of parameter a for the Orthogonal Even Coherent States.

**Figure 9.**Non-Gaussianity measures as functions of the inverse fidelity $\tau $ between the vacuum state and components of two kinds of superpositions. (

**Left**) The measures ${\delta}_{T}\left[\widehat{\rho}\right]\left(\tau \right)$ for EVSS and OECS; (

**Right**) The measures $g\left(\tau \right)$ for EVSS and OECS.

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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 Citeli, 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