The quantum computing text books and theory in general seems to have added an asymmetry in the distribution of change in phase across the components in the context of a qubit. Is there any reason for this? I know that global phase can be ignored and it allows us to assign all change to only one component. But I have observed that the impact would be different in multi-qubit contexts. For example, a controlled phase rotation between two qubits would no longer be symmetrical, if the phase distribution is symmetrical, in contradiction to what the textbook and many algorithms consider.
Is this asymmetry introduced due to any physics/hardware related problem which forbids distributing the phase change equally? Or is it only a software trick to reduce the operations (one instead of two with half change)?
I'm generally concerned about any loss of symmetry in such a beautiful and natural science. I don't think the nature itself pushes any changes entirely to one component. If it is a reference frame issue (we want to align our reference frame with one of the component for our convenience), then I'm afraid that this reference frame needs to a global one (single one for all qubits), but I see that this reference frame is local to each qubit, which appears quite artificial to me.