Comparing the three W-like states with the W state

In [Phy. Rev. Lett., 98, 260501 (2007)] and previous papers, the W-like states were used in many quantum communication schemes, distillation, teleportation and superdense coding. So far, no one has compared the W-like states with the W state. We investigate the properties of three W-like states named as |vartheta ^prime rangle, |η^prime rangle and |ξ^prime rangle. We point out that |vartheta ^prime rangle resp. $|η^prime rangle $ and $|ξ^prime rangle $ has the maximal von Neumann entanglement entropy (vNEE) S\(ρ_A\)=ln 2 resp. $S(ρ_B=\ln 2andSρ_C=\ln 2) and the maximal tangleτ_{A(BC)}=1\(resp.τ_{B(AC\)}=1andτ_{C(AB)}=1) while the W state does not. We also indicate that if some one of three qubits is traced out, then the remaining two qubits of|\vartheta ^{\prime }\rangle \(resp.|η^{\prime }\rangle and|ξ^{\prime }\rangle \) are more entangled than the two qubits of the W state by several entanglement measures. It means that the three W-like states have higher robustness against some particle loss than the W state. We show that|\vartheta ^{\prime }\rangle ,|η^{\prime }\rangle and|ξ^{\prime }\rangle $ can be suitable for perfect teleportation and superdense coding but the W state cannot.