Hermitian matrix won't work because Hermitian matrix provides only rotation on the Bloch sphere. They can't change radial vector. They changes only $\theta$ and $\phi$. Probably POVM is required to increase the radial vector without affecting the angles.

Thanks for the reply. Yes, directions are fixed. We can imagine the situation on the Bloch sphere. The required job is to change the length of Bloch vector while $\theta$ and $\phi$ are fixed. Proper measurements operator can change the length of Bloch vector without changing directions but I don't know the procedure how to choose appropriate measurement operator.

thanks sir, it's very helpful. Can you please have a look on my another similar kind of question ? I am giving the link of my question here. It will be very helpful for me. physics.stackexchange.com/questions/264227/…