Binary symplectic space of Pauli labels
= Binary symplectic space of Pauli labels
{title2=$\omega((a,b),(a',b'))=a\cdot b'+b\cdot a'$}
Modulo scalar phases, the n-qubit <Pauli group> is the additive space $\mathbb F_2^{2n}$, with label $(a,b)$ for $X^aZ^b$. Multiplication adds labels, and commutation contributes the sign $(-1)^{\omega}$. The displayed alternating form is nondegenerate. An isotropic subspace $L$ satisfies $L\subseteq L^\perp$, hence $\dim L\le n$; it labels commuting stabilizers.