Solution
= Solution
The state $|001\rangle$ has independent <stabilizer generators> $ZII$, $IZI$, and $-IIZ$. Its complete <stabilizer group> is
$$
\{III,ZII,IZI,-IIZ,ZZI,-ZIZ,-IZZ,-ZZZ\}.
$$
For $|\Phi^+\rangle\otimes|+\rangle$, take the generators $XXI$, $ZZI$, and $IIX$. Their products give
$$
\{III,XXI,ZZI,-YYI,IIX,XXX,ZZX,-YYX\}.
$$
In particular $(XX)(ZZ)=-YY$, which accounts for the two minus signs.