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If our input $x \in \{0, 1\}^{n}$ is given as a black box, we usually query an oracle as follows.
$$O_{x}|i, b \rangle = (-1)^{b x_{i}} |i, b \rangle$$
$i = \{1, 2, \cdots, n \}$ is the index of the input we are querying. $x_{i}$ is the value at that index. $b = \{0, 1\}$ is an arbitrary Boolea...