Greenberger–Horne–Zeilinger state
In physics, in the area of quantum information theory, a Greenberger–Horne–Zeilinger state is a certain type of entangled quantum state which involves at least three subsystems (particles). It was first studied by Daniel Greenberger, Michael Horne and Anton Zeilinger in 1989. Extremely non-classical properties of the state have been observed.
The GHZ state is an entangled quantum state of M > 2 subsystems. In the case of each of the subsystems being two-dimensional, that is for qubits, it reads
In simple words it is a quantum superposition of all subsystems being in state 0 with all of them being in state 1 (states 0 and 1 of a single subsystem are fully distinguishable).
The simplest one is the 3-qubit GHZ state:
This state is non-biseparable and is the representative of one of the two non-biseparable classes of three-qubit states (the other being the W state) which cannot be transformed (not even probabilistically) into each other by local quantum operations. Thus and represent two very different kinds of tripartite entanglement. The W state is, in a certain sense "less entangled" than the GHZ state; however, that entanglement is, in a sense, more robust against single-particle measurements, in that, for an N-qubit W state, an entangled (N-1) qubit state remains after a single particle measurement. By contrast, certain measurements on the GHZ state collapse it into a mixture or a pure state.
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