Nonclassicality and entanglement properties of non-Gaussian entangled states via a superposition of number-conserving operations

We theoretically investigate the nonclassicality and entanglement properties of non-Gaussian entangled states generated by using a number-conserving generalized superposition of products (GSP), i.e., \(\left( saa^{\dag }+ta^{\dag }a\right) ^{m}\) with \(s^{2}+t^{2}=1\) on each mode of an input two-mode squeezed coherent (TMSC) state. The simulation results show that, compared to the typical two-mode squeezed vacuum state, the usage of small coherent amplitude is conductive to offering an opportunity for not only effectively enhancing the nonclassicality in terms of antibunching effect and Wigner function, but also significantly improving the entanglement quantified by Einstein–Podolsky–Rosen correlation and Hillery–Zubairy correlation. For the increase of the number of operations, the region of both the existing antibunching effect and the improved entanglement decreases, but this region of the improved teleportation fidelity and the negative distribution of the Wigner function is on the increase. Under an ideal Braunstein and Kimble teleportation protocol, when the generated states are treated as an entangled resource, the optimal teleportation fidelity can be achieved by taking a suitable squeezing parameter and the number of operations for the optimal choices of s. In order to highlight the advantages of the use of the GSP-embedded TMSC, under the same parameters, we also make a comparison about the performances of both the entanglement and the fidelity for different non-Gaussian entangled states, involving the photon-subtracted-then-added TMSC states and the photon-added-then-subtracted TMSC states. It is found that in the regime of small squeezing values, both of the entanglement and the fidelity for the generated states can perform better than the other cases.