Pauli group P_n for n qubits is the group consisting of n-fold tensor products of Pauli matrices I, X, Y, and Z $I=\begin{pmatrix}1&0\\0&1\end{pmatrix}, X=\begin{pmatrix}0&1\\1&0\end{pmatrix}, Y=\begin{pmatrix}0&-i\\i&0\end{pmatrix}, Z=\begin{pmatrix}1&0\\0&-1\end{pmatrix}$. along with multiplicative factors  ± 1,  ± i with matrix multiplication as a group operation. NielsenChuang

In particular for one qubit system we have

P₁ = { ± I,  ± iI,  ± X,  ± iX,  ± Y,  ± iY,  ± Z,  ± iZ}.

Category:Mathematical Structure