In general I understand Grover's algorithm, how we can think of two separated state spaces, a space $|\alpha\rangle$ with no solutions and a space $|\beta\rangle$ with only solutions, and how the Grover operator rotates the state $|\psi\rangle$ into the solution space $|\beta\rangle$.
- In the implementation of grover, we use $|000...0\rangle$ as the state to reflect about. The math and how the inversion around the mean operator is constructed, this appears to be an easy and elegant way. The math adds up. I'm not clear how to justify the use of this particular state. Can't we use others as axes, and if not, why not?