Pauli group (original) (raw)
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 and : . The Pauli group is generated by the Pauli matrices, and like them it is named after Wolfgang Pauli. The Pauli group on qubits, , is the group generated by the operators described above applied to each of qubits in the tensor product Hilbert space . As an abstract group, is the central product of a cyclic group of order 4 and the dihedral group of order 8.
| Property | Value |
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| dbo:abstract | 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 and : . The Pauli group is generated by the Pauli matrices, and like them it is named after Wolfgang Pauli. The Pauli group on qubits, , is the group generated by the operators described above applied to each of qubits in the tensor product Hilbert space . As an abstract group, is the central product of a cyclic group of order 4 and the dihedral group of order 8. 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. (en) |
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| rdfs:comment | 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 and : . The Pauli group is generated by the Pauli matrices, and like them it is named after Wolfgang Pauli. The Pauli group on qubits, , is the group generated by the operators described above applied to each of qubits in the tensor product Hilbert space . As an abstract group, is the central product of a cyclic group of order 4 and the dihedral group of order 8. (en) |
| rdfs:label | Pauli group (en) |
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