Greenberger-Horne-Zeilinger state
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In physics, in the area of quantum information theory, a Greenberger-Horne-Zeilinger state is a certain type of entangled quantum state.
Definition
The GHZ state is an entangled quantum state in an M dimensions:- [|GHZ\rangle = \frac + |1\rangle^}}.]
Properties
Apparently there is no standard measure of multi-partite entanglement, but many measures define the GHZ to be maximally entangled.Another important property of the GHZ state is that when we trace over one of the three systems
- [Tr_3\left((|000\rangle + |111\rangle)(\langle 000|+\langle 111|) \right) = |00\rangle \langle 00| + |11\rangle \langle 11|]
On the other hand, if we were to measure any of subsystems we will leave behind either [|00\rangle] or [|11\rangle] which are not entangled. Thus, we say that the GHZ is maximally entangled. This is unlike the W state which leaves bipartite entanglements even when we measure one of its subsystems.
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