qudits systems
which reduces to the Bell state 




|


Φ

+


⟩


{\displaystyle |\Phi ^{+}\rangle }

 for 



M
=
2


{\displaystyle M=2}

. The traditional GHZ state was defined for 



M
=
3


{\displaystyle M=3}

. GHZ states are occasionally extended to qudits, i.e., systems of d rather than 2 dimensions.
