This idea is new to me. My limited understanding is that the macroscopic butterfly effect is related to non linear system effects....and slightly different initial conditions....but here it seems the initial condition is fixed, so how does the Hamiltonian change...what does that mean?? Is this 'quantum butterfly' effect saying anything about our linear [superposition] principles in QM?

Jae-Seung Lee and A. K. Khitrin, Quantum amplifier: Measurement with entangled spins, J. Chem. Phys. 121, 3949 (2004). http://dx.doi.org/10.1063/1.1788661