I saw in a class that star state and GHZ state are local-Clifford equivalent (Hadamard on n-1 qubits for a n star state).

But then, when I wanted to draw a GHZ state and check on the litterature whether or not I got it right, it seemed as a lot of representations I came across of GHZ graph state were simply star graph state :

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and I would have expected something like the following instead, especially because GHZ state are supposed to be maximally entangled state :

enter image description here

Could you enlighten me ?

And while I am it, is there an intuitive way of understanding the action of a Hadamard on a graph state (ex: Local complementation) ?

Many thanks in advance!!



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