= Collective-unitary covariance of the two-qubit singlet
{title2=$(U\otimes U)|s\rangle=(\det U)|s\rangle$}
For $|s\rangle=(|01\rangle-|10\rangle)/\sqrt2$ and any two-by-two <unitary matrix>, expand the two columns of $U$. The equal-index coefficients cancel, and the coefficient of $|01\rangle-|10\rangle$ is the determinant. Its modulus is one, so a common change of qubit basis preserves the <spin singlet state> up to a <global phase>. The density projector is exactly invariant.
Back to article page
