Quantum entanglement of an entangled coherent state：Role of particle losses

We analyze entanglement properties of entangled coherent state （ECS）, ｜α,0） 1,2 ＋｜0,α） 1,2, with and without photon losses. By separating the coherent state into ]a） = co｜0） ＋ √-Co2｜α）, we derive exact results of the logarithmic negativity EN, which quantifies the degree of entanglement between the two bosonic modes. Without particle losses, E~ = 1 for the NOON state; while for the ECS, E jr increases from 0 to 1 as ｜α｜-→∞. In the presence of photon losses, we find that the ECS with large enough photon number is more robust than that of the NOON state. An optimal ECS is obtained by maximizing E~ with respect to l a 12.