Psy-Kosh, the amplitudes of everything everywhere could be changing by a constant modulus and phase, without it being noticed. But if it were possible for you to carry out some physical process that changed the squared modulus of the LEFT blob as a whole, without splitting it and without changing the squared modulus of the RIGHT blob, then you would be able to use this physical process to change the ratio of the squared moduli of LEFT and RIGHT, hence control the outcome of arbitrary quantum experiments by invoking it selectively.

It would be an Outcome Pump.

Controllable unitarity violation wouldn't just let you win the lottery, it would let you communicate faster than light, by forcing a particular outcome in a quantum entanglement, Bell's Inequality type situation.