W state (source code)
= W state
{c}
{title2=$|W_n\rangle=|D_1^n\rangle$}
The $n$-<qubit> <W state> is the <Dicke state> with one excitation:
$$
|W_n\rangle=\frac1{\sqrt n}\sum_{j=1}^n|0\cdots010\cdots0\rangle=|D_1^n\rangle.
$$
For three <qubits> it is $(|001\rangle+|010\rangle+|100\rangle)/\sqrt3$. Its <reduced density matrix> on any one <qubit> is $\operatorname{diag}((n-1)/n,1/n)$, from the <Dicke state> recursion. For $n>1$ both diagonal entries are nonzero, so that <qubit> is entangled with the rest: a pure <product state> would have a pure marginal. A <symmetric-arm reduction of an exchange Hamiltonian> supplies a dynamical preparation from one initial excitation.
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