  Performing non-Gaussian operations, namely photon addition, photon
subtraction, photon-addition-then-subtraction, photon-subtraction-then-addition
can successfully enhance the fidelity of the continuous-variable quantum
teleportation. However, a shortcoming of these non-Gaussian resources is that
they are probabilistic in nature. In this article, we investigate the success
probability of the non-Gaussian resources for optimal performance of the ideal
teleportation protocol. To this end, we first derive the analytical expression
for the two-mode entangled channel having $f$-deformed displaced Fock state or
photon-added displaced Fock state or photon-subtracted displaced Fock state at
one port and vacuum at another port of a symmetric beam-splitter. The
generalized displaced Fock states are obtained by replacing the conventional
bosonic functions by the nonlinear $f$-deformed operators such as $A=af(a^\dag
a)$ and $B=af(a^\dag a)^{-1}$. The Wigner characteristic functions describing
these three aforementioned non-Gaussian states are determined and utilized to
attain the teleportation fidelity for input coherent and squeezed vacuum
states. It is found that the nonlinear substitution leads to an enhancement in
teleportation fidelity beyond the threshold limit. Moreover, the entangled
photon-subtracted displaced Fock state demonstrates maximum efficiency as a
quantum channel for teleporting single-mode coherent and squeezed states. We
provide the squeezing regime values corresponding to the optimal performance of
the non-Gaussian states considered, which will be of significant interest to
the experimental fraternity. Further, we show that the entangled photon-added
displaced Fock states have larger amount of entanglement but the entangled
photon-subtracted displaced Fock states have stronger Einstein-Podolsky-Rosen
correlation.
