Generation of Non-Gaussian States in the Squeezed State Entanglement Scheme

Abstract: The paper considers the possibility of generating different non-Gaussian states using the entangled state photon measurement scheme. In the paper, we have proposed a way to explicitly find the wave function and the Wigner function of the output state of this scheme. Moreover, the solutions found are not restricted to any particular case, but have maximum generality (depend on the number of measured photons and on all parameters of the scheme). Such a notation allowed us to carry out a complete analysis of the output states, depending on the scheme parameters. Using explicit expressions, we have analyzed the magnitude of non-Gaussianity of the output states, and we have revealed which particular states can be obtained in the proposed scheme. We have considered in detail a particular case of measurement (single photon measurement) and have shown that using explicit expressions for the output state wave function one can find scheme parameters to obtain states suitable for quantum error correction codes with a large fidelity value and high probability. The Schrodinger cat state with amplitude $\alpha=2$ can be obtained with fidelity $F \approx 0.88$ and probability 18 percent, and the squeezed Schrodinger cat state ($\alpha=0.5$, $R=1$) with fidelity $F \approx 0.98$ and probability 22 percent.