High success standard quantum teleportation using entangled coherent state and two-level atoms in cavities

We propose here a new idea for quantum teleportation of superposed coherent state which circumvents the problem performing non-unitary $$Z_c=|\alpha \rangle \langle \alpha |-|-\alpha -\alpha |$$ operation on qubit. The receiver only requires to perform either no unitary or $$\pi $$ phase shift in order recreate information state. use entangled resource $$\sim |\alpha ,\frac{\alpha }{\sqrt{2}}\rangle -|-\alpha ,-\frac{\alpha contrast with usual ,\alpha ,-\alpha -(both states unnormalized). Bob receives is then superposition $$|\pm \frac{\alpha . mixes these even odd involving obtain two-mode one |I,0\rangle \pm |0,I\rangle , $$|I\rangle being obtains teleported by using interaction modes two cavities resonant two-level atoms. This scheme results average fidelity $$\simeq 0.95$$ $$|\alpha |^2 \simeq 10$$ increases |^2$$ and tends 1 asymptotically, varying as $$1-\frac{\pi ^2}{16|\alpha |^2}+\frac{\pi ^2(\pi ^2+8)}{256|\alpha |^4}$$ large values