Continuous variable quantum teleportation, $U(2)$ invariant squeezing and non-Gaussian resource states

We investigate the role of quadrature squeezing in the quantum teleportation protocol for coherent states, using non-Gaussian resource states. For the two-mode systems, the non-Gaussian resource states that we use are obtained by an experimentally realizable scheme of photon subtraction, photon addition, and photon catalysis, on the two-mode squeezed vacuum, and two-mode squeezed thermal states. We first analyze the non-classical attribute of quadrature squeezing in these generated non-Gaussian states using the $U(2)$ invariant squeezing approach, which allows us to account for all possible quadratures. We then show that the presence of such non-classicality in non-Gaussian resource states is not necessary for successful quantum teleportation, a finding which is at variance with an earlier result in this direction. This result is important since it demonstrates how non-classicality other than quadrature squeezing present in the resource can be utilized for quantum teleportation.