Solution
= Solution
The controlled-NOT leaves computational-basis signals unentangled:
$$
|0\rangle_A|0\rangle_E\mapsto|00\rangle,\qquad
|1\rangle_A|0\rangle_E\mapsto|11\rangle.
$$
For the two Hadamard-basis choices it gives
$$
|+\rangle_A|0\rangle_E\mapsto
\frac{|00\rangle+|11\rangle}{\sqrt2}=|\phi^+\rangle,
$$
$$
|-\rangle_A|0\rangle_E\mapsto
\frac{|00\rangle-|11\rangle}{\sqrt2}=|\phi^-\rangle.
$$
Both outputs are <Bell state>[maximally entangled Bell states].