Unitarity

The probability should continue to sum to one.

If this is true, and it must be, we say that the time evolution of the wave function is unitary, and this unitarity is a foundational assumption in all formulations of quantum mechanics and quantum field theories.

Unitarity is a non-negotiable statement about how probability works, but the condition also ensures time reversal symmetry and conservation of information.

It's not straightforward to explain without getting into some hairy math, but the upshot is that quantum states must remain independent of each other in order to preserve probability.

Two independent quantum states can't evolve into the exact same quantum state.