I know how to create coherence between two states if I have a pure state. For example if the system is in pure state $|1\rangle = \begin{bmatrix}1\\0 \\\end{bmatrix}$ then density matrix is given by $\rho_o = \begin{bmatrix}1 & 0\\0 & 0\\\end{bmatrix}$. To create coherence we can apply $\sqrt{NOT} = \frac{1}{2}\begin{bmatrix}1+i & 1-i\\1-i & 1+i\\\end{bmatrix}$ gate and the density matrix becomes $\rho = \sqrt{NOT}\rho_o\sqrt{NOT'} = \frac{1}{2}\begin{bmatrix}1 & 1\\1 & 1\\\end{bmatrix}$. The $\sqrt{NOT}$ gate is equivalent to applying a $\frac{\pi}{2}$ pulse and we can see a superposition and coherence is created in the system.
I was wondering if one can create coherence if we start from a mixed state $\rho_o = \frac{1}{2}\begin{bmatrix}1 & 0\\0 & 1\\\end{bmatrix}$. Is there some quantum gate or any pulse sequence to achieve coherence in system starting from mixed state?
EDIT- Using Unitary Transformations only