Lecture 3. Pauli group and stabilizer states

In this Lecture we study algebraic properties of the Pauli group and stabilizer subgroups for the case of multiqubit systems. The Pauli group is quite simple to describe: we can think of it as “abelian” modulo phases. Any two Pauli operators either commute or anticommute; non-identity Pauli operators have zero trace. A stabilizer subgroup in a Pauli group is an abelian subgroup consisting of self-adjoint operators and not containing $-I$. Stabilizer subgroups have a set of generators, the choice of which determines the stabilizer tableau. Maximal stabilizer groups correspond to an important class of stabilizer states.