The density matrix for mixed state qubits and hyperbolic geometry (pp513-514)
       A.A. Ungar
          doi: https://doi.org/10.26421/QIC2.6-5
Abstracts: Density matrices for mixed state qubits, parametrized by the Bloch vector in the open unit ball of the Euclidean 3-space, are well known in quantum information and computation theory. By presenting new identities for the qubit density matrix we indicate its intimate relationship with M\"obius addition and scalar multiplication. The latter, in turn, form the algebraic setting for the Poincar\'e ball model of hyperbolic geometry so that, as a result, the qubit density matrix is linked to hyperbolic geometry.
Key words: qubit, density matrix, Mobius addition, hyperbolic geometry