Is it possible to perform an operation on two qubits with initial states as follows:
$$q_1: 1/\sqrt(2)(|0\rangle + exp(0.a_1a_2a_3)|1\rangle)$$ $$q_2: 1/\sqrt(2)(|0\rangle + |1\rangle)$$
To resultant state:-
$$q_1: 1/\sqrt(2)(|0\rangle + exp(0.a_1a_2)|1\rangle)$$ $$q_2: 1/\sqrt(2)(|0\rangle + exp(0.a_3)|1\rangle)$$
Without knowing the value of $a_3$. Where $a_1,a_2,a_3 ∈ [0, 1].$
The idea is to shift the phase of $q_1$ by $exp(-0.00a_3)$ and $q_2$ by $exp(0.a_3)$ with the unitary operation not being aware of the value of $a_3$.