According to bloch sphere interpretation, any point on the surface of the sphere corresponds to a pure state and any point inside the sphere corresponds to a mixed state. Suppose you have a point inside the bloch sphere C corresponding to a mixed state. Draw a ray connecting C and origin O of the bloch sphere. Now extend this ray OC such that we get some point C' on the surface of the sphere. Now C' = cC for which c is a real number.
So can we say that the mixed state corresponding to point C when normalized becomes a pure state? Or is there a problem with this logic?