# Pauli group

Pauli group Pn for n qubits is the group consisting of n-fold tensor products of Pauli matrices I, X, Y, and Z $I=\begin{pmatrix}1&amp;0\\0&amp;1\end{pmatrix}, X=\begin{pmatrix}0&amp;1\\1&amp;0\end{pmatrix}, Y=\begin{pmatrix}0&amp;-i\\i&amp;0\end{pmatrix}, Z=\begin{pmatrix}1&amp;0\\0&amp;-1\end{pmatrix}$. 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