Mapping two-qubit operators onto projective geometries
The link between a quantum spin 1/2 and its associated su(2) algebra of Pauli spin matrices with Clifford algebra and quaternions is well known. A pair of spins or qubits, which are important throughout the field of quantum information for describing logic gates and entangled states, has similarly an su(4) algebra. We develop connections between this algebra and its subalgebras with the projective plane of seven elements (also related to octonions) and other entities in projective geometry and design theory. © 2009 The American Physical Society.
Publication Source (Journal or Book title)
Physical Review A - Atomic, Molecular, and Optical Physics
Rau, A. (2009). Mapping two-qubit operators onto projective geometries. Physical Review A - Atomic, Molecular, and Optical Physics, 79 (4) https://doi.org/10.1103/PhysRevA.79.042323