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The standard reversible oracle embedding writes f into an ancilla register via U_f|x>|y> = |x>|y XOR f(x)>. What happens when you apply U_f twice in a row?
It computes f(f(x)) on the input register
It returns the original state (U_f is its own inverse)
It doubles the phase of every component
It erases the input register |x>
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