Comment on “Teleportation of two-mode squeezed states”
Guangqiang He, Jingtao Zhang · Physical Review A · 2011
We investigate the teleportation scheme of two-mode squeezed states proposed by Adhikari et al. [S. Adhikari et al., Phys. Rev. A 77, 012337 (2008)]. It uses four-mode entangled states to teleport two-mode squeezed states. The fidelity between the original two-mode squeezed states and teleported ones is calculated. The maximal fidelity value of Adhikari's protocol is $0.38$, which is incompatible with the fidelity definition with the maximal value 1. In our opinion, one reason is that they calculate the fidelity for multimodes Gaussian states using the fidelity formula for single-mode ones. Another reason is that the covariance matrix of output states should be what is obtained after applying the linear unitary Bogoliubov operations (two cascaded Fourier transformations) on the covariance matrix given in Eq. (12) in their paper. These two reasons result in the incomparable results. In addition, Adhikari's protocol can be simplified to be easily implemented.