 Greenberger–Horne–Zeilinger state

A GHZ state is a multipartite entangled state with coherent amplitudes linking the alternatives in which all qubits are $0$ and all are $1$.

The three-qubit GHZ state is

Computational-basis measurements give only $000$ and $111$, each with probability one half. A classical mixture of those strings gives the same probabilities, but lacks the off-diagonal quantum coherence. For the displayed state, $⟨X\otimes X\otimes X⟩=1$, whereas it is zero for the mixture. Tracing out one qubit leaves a classically correlated mixture of $|00⟩$ and $|11⟩$. ^[ref]

The Greenberger–Horne–Zeilinger (GHZ) state is a specific type of entangled quantum state that involves multiple particles, typically three or more. Named after Daniel Greenberger, Michael A. Horne, and Anton Zeilinger, this state serves as an important example in quantum mechanics, particularly in discussions of entanglement, non-locality, and the foundations of quantum theory.