 W state

The $n$-qubit W state is the Dicke state with one excitation:For three qubits it is $(|001⟩+|010⟩+|100⟩)/\sqrt{3}$. Its reduced density matrix on any one qubit is $\mathrm{diag}((n-1)/n,1/n)$, 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.

The W state is a type of quantum state that is significant in the study of quantum information and quantum computing. Specifically, the W state is a kind of entangled state involving multiple qubits (quantum bits). It is known for its robustness in maintaining entanglement among particles. For a system of \( n \) qubits, the W state can be defined as: \[ |W_n\rangle = \frac{1}{\sqrt{n}} (|100...