The effect of channel decoherence on entangled coherent states: A theoretical analysis

We analyse decoherence properties of entangled coherent states (ECSs) due to channel losses, and compare to the performance of bi-photon Bell states. By employing the concept of "entanglement of formation" (EOF), the degradation of fidelity and degree of entanglement are calculated. Two situations are considered: (1) asymmetric and (2) symmetric noise channel. In the first case, only the lower bound of EOF is given. However, in the latter case, we have obtained an explicit expression of concurrence (and then EOF) and found surprisingly our result is just incompatible with that of [Phys. Rev. A \textbf{82}, (2010) 062325] in the limit of $\alpha\rightarrow0$. We demonstrate that entangled coherent states with sufficient small amplitudes are more robust against channel decoherence than biphoton entangled states in both cases.