A maximally entangled quantum state of three or more particles, a fundamental resource in quantum information.The Greenberger–Horne–Zeilinger (GHZ) state is a quantum state of three or more particles that is maximally entangled, meaning the particles' properties are correlated in a way that cannot be described by any classical theory. For three particles, the GHZ state is famously 'all or nothing': measuring any two particles in a certain basis yields a definite outcome for the third, yet the state is not a product of any two-particle entanglements. GHZ states are fundamental for testing the foundations of quantum mechanics, such as the violation of local realism, and are a key resource for quantum computing, quantum communication, and quantum metrology.
The state was introduced in 1989 by Daniel Greenberger, Michael Horne, and Anton Zeilinger, who showed that for three or more particles, quantum mechanics predicts a contradiction with local realism that is deterministic (no statistical averaging needed), unlike the Bell inequalities for two particles.
In a GHZ state, the particles are prepared in a superposition of all being in one state (e.g., spin up) and all being in the opposite state (e.g., spin down). For three particles, this is written as |000⟩ + |111⟩ (up to normalization). The entanglement is 'genuine' because it cannot be reduced to pairwise entanglement: the state is not separable into any combination of two-particle and single-particle states. Measurements on one particle instantly affect the state of the others, but the correlations are stronger than any classical hidden-variable model can explain, as demonstrated by the GHZ theorem.
GHZ states are used in quantum error correction codes, multiparty quantum cryptography, and as a resource for quantum teleportation and entanglement swapping in quantum networks.
In 2023, researchers created a GHZ state with 120 superconducting qubits, setting a record for the largest genuine multipartite entanglement in a solid-state system.













