Past exam of the mathematics course of the University of Cambridge / 2022 / iii / Paper 324 / 2 / ii / Solution

The state $|001⟩$ has independent stabilizer generators $ZII$, $IZI$, and $-IIZ$. Its complete stabilizer group isFor $|{\Phi }^{+}⟩\otimes |+⟩$, take the generators $XXI$, $ZZI$, and $IIX$. Their products giveIn particular $(XX)(ZZ)=-YY$, which accounts for the two minus signs.