  We theoretically analyze the Einstein-Podolsky-Rosen (EPR) correlation, the
quadrature squeezing, and the continuous-variable quantum teleportation when
considering non-Gaussian entangled states generated by applying multiple-photon
subtraction and multiple-photon addition to a two-mode squeezed vacuum state
(TMSVs). Our results indicate that in the case of the
multiple-photon-subtracted TMSVs with symmetric operations, the corresponding
EPR correlation, the two-mode squeezing degree, the sum squeezing, and the
fidelity of teleporting a coherent state or a squeezed vacuum state can be
enhanced for any squeezing parameter r and these enhancements increase with the
number of subtracted photons in the low-squeezing regime, while asymmetric
multiple-photon subtractions will generally reduce these quantities. For the
multiple-photon-added TMSVs, although it holds stronger entanglement, its EPR
correlation, two-mode squeezing, sum squeezing, and the fidelity of a coherent
state are always smaller than that of the TMSVs. Only when considering the case
of teleporting a squeezed vacuum state does the symmetric photon addition make
somewhat of an improvement in the fidelity for large-squeezing parameters. In
addition, we analytically prove that a one-mode multiple-photon-subtracted
TMSVs is equivalent to that of the one-mode multiple-photon-added one. And
one-mode multiple-photon operations will diminish the above four quantities for
any squeezing parameter r.
