The non-deterministic quantum logic operation and teleportation of a vacuum and single photon superposition state via parametric amplifiers

We firstly present an all-optical scheme to implement the non-deterministic quantum logic operation of Knill, Laflamme and Milburn (Nature, 409, 46-52(2001)). In our scheme, squeezed vacuum state is acted as auxiliary state instead of single photon resources. Then we demonstrate that same setup can be used to teleport a superposition of vacuum and single photon state of the form $\alpha|0>+\beta|1>$ and a superposition of vacuum and single polarized photon state of the form $\alpha|0>+\beta|H>+\gamma|V>$.