A Greenberger-Horne-Zeilinger state, or GHZ state, is a multipartite entangled state of 
qubits of the form
 |
The two terms are orthogonal unit vectors in the tensor product space 
, so the state is normalized. Across any division
into two nonempty groups of qubits, this state has Schmidt
rank two and hence exhibits quantum entanglement.
For three qubits,
 |
Its perfect correlations under products of Pauli matrices yield the Greenberger-Horne-Zeilinger theorem, a contradiction with predetermined local outcomes that does not require an inequality (Greenberger et al. 1990).
