W State

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A W State is a collective spin state with one ‘excitation’ as compared to a coherent spin state which is fully aligned. With all but one spin aligned in the x-direction, the state can be written:

$|\textrm{W}\rangle = \frac{1}{\sqrt{N}}|\downarrow \uparrow \uparrow \cdots \uparrow\rangle + | \uparrow \downarrow \uparrow \cdots \uparrow\rangle+\cdots+|\uparrow\cdots \uparrow \downarrow\rangle$

This is a particular example of a Dicke State with maximal $\vec{F}^2$ eigenvalue of $F (F + 1)$ , but with $F x$ eigenvalue of $F - 1$ .