# Global phase Given a qubit $|\psi\rangle$ and any $\theta\in\mathbb{R}$ , the qubit $e^{i\theta}|\psi\rangle$ is physical indistinguishable from $|\psi\rangle$. Because there is no physical measure to differentiate them. For unitary operation $U$ we have $Ue^{i\theta}|\psi\rangle=e^{i\theta}U|\psi\rangle$ and so physical indistinguishable from $U|\psi\rangle$. For example: $Y=-iXZ$ and so $Y$ acts the same as $XZ$ on qubit i.e., $Y=XZ$ up to global phase. ## Created 2026-04-14 18:10