The GHZ state is a four state entanglement. The symmetry is a bit more 
complicated. The entanglement is a quotient state and a typical form is 

G/H = SO(8)/SO(4)xSO(4)

in 16 dimensions. This in a rule of thumb way captures the 2^4 possible 
state configurations. 

The GHZ state then gives a larger set of probability polynomials, but in 
the end it really gives much the same result as the standard EPR binomial 
entanglement. We can say in some sense that maybe there is some reality to 
the evolution of a quantum system, but we have no way of unobtrusively 
accessing that reality. If we verify the evolution of the state we lose its 
coherence. Even with quantum erasers or weak measurements there is some 
obtrusion.

LC

On Friday, December 1, 2017 at 4:25:17 AM UTC-6, scerir wrote:
>
> BTW, how is this [1] [2] intensionality, or contextuality, or wholeness, 
> or undecidibility, or whatever - and related difficulties regarding the 
> existence of "elements of reality" [3] - understandable within (postulates 
> of) Quantum Mechanics (and especially within ontological interpretations 
> like MWI)?
>
> [1] https://arxiv.org/abs/0712.0921
>
> [2] http://www.math.zju.edu.cn/wjd/notespapers/3-2.pdf
>
> [3] “”if, without in any way disturbing a system, we can predict with 
> certainty (i.e., a probability equal to unity) the value of a
> physical quantity, then there exists an element of physical reality 
> corresponding to this physical quantity.” ---EPR
>

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