Near-complete teleportation of a superposed coherent state

Abstract

The four Bell-type entangled coherent states, $\ensuremath{\mid}\ensuremath{\alpha}⟩\ensuremath{\mid}\ensuremath{-}\ensuremath{\alpha}⟩\ifmmode\pm\else\textpm\fi{}\ensuremath{\mid}\ensuremath{-}\ensuremath{\alpha}⟩\ensuremath{\mid}\ensuremath{\alpha}⟩$ and $\ensuremath{\mid}\ensuremath{\alpha}⟩\ensuremath{\mid}\ensuremath{\alpha}⟩\ifmmode\pm\else\textpm\fi{}\ensuremath{\mid}\ensuremath{-}\ensuremath{\alpha}⟩\ensuremath{\mid}\ensuremath{-}\ensuremath{\alpha}⟩$, can be discriminated with a high probability using only linear optical means, as long as $\ensuremath{\mid}\ensuremath{\alpha}\ensuremath{\mid}$ is not too small. Based on this observation, we propose a simple scheme to almost completely teleport a superposed coherent state. The nonunitary transformation that is required to complete the teleportation can be achieved by embedding the receiver's field state in a larger Hilbert space consisting of the field and a single atom and performing a unitary transformation on this Hilbert space.