We discuss the canonical form for a pure state of three identical bosons in two modes, and classify its entanglement correlation into two types, the analogous Green-Horne-Zeilinger and the $W$ types as well known in systems of three distinguishable qubits. We have performed a detailed study of two important entanglement measures for such a system, the concurrence $\mathcal{C}$ and the triple entanglement measure $\tau$. We have also calculated explicitly the spin squeezing parameter $\xi$ and the result shows that the $W$ state is the most “antisqueezing” state, for which the spin-squeezing parameter cannot be regarded as an entanglement measure.

• Received 17 November 2004

DOI:https://doi.org/10.1103/PhysRevA.71.042317