Comparing the three W-like states with the W state

Abstract

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 $|{\vartheta }^{\prime }⟩$, $|\hat{I}{\cdot }^{\prime }⟩$ and $|\hat{I}{¾}^{\prime }⟩$. We point out that $|{\vartheta }^{\prime }⟩$ (resp. $|\hat{I}{\cdot }^{\prime }⟩$ and $|\hat{I}{¾}^{\prime }⟩$) has the maximal von Neumann entanglement entropy (vNEE) $S(\ddot{I}{}_A)=\ln 2$ (resp. $S(\ddot{I}{}_B)=\ln 2$ and $S(\ddot{I}{}_C)=\ln 2$) and the maximal tangle $\ddot{I}{„}_{A(BC)}=1$ (resp. $\ddot{I}{„}_{B(AC)}=1$ and $\ddot{I}{„}_{C(AB)}=1$) 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 $|{\vartheta }^{\prime }⟩$ (resp. $|\hat{I}{\cdot }^{\prime }⟩$ and $|\hat{I}{¾}^{\prime }⟩$) 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 $|{\vartheta }^{\prime }⟩$, $|\hat{I}{\cdot }^{\prime }⟩$ and $|\hat{I}{¾}^{\prime }⟩$ can be suitable for perfect teleportation and superdense coding but the W state cannot.

11 pages

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