The Global Phase
Usually, you'd expect quantum phases to matter. But global phases do not. Why is that?
What happens when you apply a Z-Gate to the state |1⟩?
Usually, you’d expect the Vector in the Bloch Sphere swing to a new position or flip across an axis. Right?
The Z-Gate turns the Quantum State Vector around the Z-axis by 180°.
But in state |1⟩, the Quantum State Vector resides on the Z-axis. So, apparently, nothing seems to move. The Vector in the Bloch Sphere looks unchanged.
Could that be correct? Did you ever wonder if the state secretly rotated around its own axis in some invisible way?