I have a basic question about the definition of the Greenberger–Horne–Zeilinger state , which is defined as the maximally entangled state. Why is it only considered applicable for subsystems $M > 2$, why would the definition not apply or why is it not preferable to consider states where $M = 2$?

  • $\begingroup$ I've removed the second half of your post as it has no bearing on the initial question or with the title. You're perfectly welcome to ask it separately, of course. $\endgroup$ – Emilio Pisanty Apr 16 '18 at 13:32

A GHZ in $M=2$ would be $|00\rangle+|11\rangle$. Sure you could still call it a GHZ, but it is not very useful because this state already has a name: it's a Bell state.

A standard reference to understand entanglement and how it is measured is Gühne and Toth 2008.

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