'Difference' between two quaternions

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I'm working in Ogre, but it's a general quaternion problem.

I have an object, to which I apply a rotation quaternion Q1 initially. Later, I want to make it as if I initially rotated the object by a different quaternion Q2.

How do I calculate the quaternion which will take the object, already rotated by Q1, and align it as if all I did was apply Q2 to the initial/default orientation? I was looking at (s)lerping, but I am not sure if this only valid on orientations rather than rotations?

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