Pauli group

In physics and mathematics, the Pauli group

on 1 qubit is the 16-element matrix group consisting of the 2 × 2 identity matrix

and all of the Pauli matrices together with the products of these matrices with the factors

: The Pauli group is generated by the Pauli matrices, and like them it is named after Wolfgang Pauli.

The Pauli group on

, is the group generated by the operators described above applied to each of

qubits in the tensor product Hilbert space

factor in any tensor position can be moved to any other position.

As an abstract group,

is the central product of a cyclic group of order 4 and the dihedral group of order 8.

[1] The Pauli group is a representation of the gamma group in three-dimensional Euclidean space.

It is not isomorphic to the gamma group; it is less free, in that its chiral element is

whereas there is no such relationship for the gamma group.

2. https://arxiv.org/abs/quant-ph/9807006 This quantum mechanics-related article is a stub.

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