is one of the two nonequivalent entangled 3-qubit states, the other being the GHZ state

.

W-states (evidently named after Wolfgang Dür) are considered to have more robust entanglement than GHZ-states (named after Greenberger, Horne and Zeilinger). Two qubits of a W-state remain entangled even if one qubit is lost (or measured), while a GHZ state collapses.

The W-state can be created by the quantum computer circuit shown in the graphic. Click "show intermediate states" to see the quantum states of the 3-qubit system at each stage. More information is given in Details. Alice, Bob and Charlie each receive one of the three entangled qubits in the W-state. They are located far apart, at spacelike separations from one another, so that no individual action by any of the three can be causally connected to either of the other two.

We describe some experiments showing accord with Bell's theorem, according to which no classical theory of local hidden variables can reproduce the predictions of quantum mechanics. Suppose Alice, Bob and Charlie are provided with devices that can measure either

or

on their qubit. (These might, for example, be Stern–Gerlach analyzers.) A

measurement will result in one of the base states

or

, while a

measurement will give one of the alternative base states

or

. The two bases are related by

,

.

In experiment 1, all three observers measure

. The result will be one

and two

s. Thus any two measurements unambiguously determine the result of the third. In experiment 2, Alice again measures

, while Bob and Charlie now measure

. Assume that Alice finds

. The W-state after Alice's measurement reduces to

. Re-expressing the last two qubits in the

basis, this transforms to

. This implies that Bob and Charlie will obtain either two

s or two

s. In the case that Alice finds

, no relevant information ensues: Bob and Charlie obtain random combinations of

s and

s.

A new experiment can be run by choosing a different seed.