Deutsch-Jozsa test with an arbitrary uniform-state unitary
= Deutsch-Jozsa test with an arbitrary uniform-state unitary
{c}
If $F|0\rangle=N^{-1/2}\sum_i|i\rangle$, then applying a phase oracle followed by $F^{-1}$ gives amplitude
$$
\frac1N\sum_i(-1)^{f(i)}
$$
on $|0\rangle$. It has modulus one for a constant Boolean function and vanishes for a balanced one.