The density maxtrix for mixed state qubits and hyperbolic geometry

  • Authors:

  • Abraham A. Ungar

  • Affiliations:

  • Department of Mathematics, North Dakota State University, Fargo, ND

  • Venue:
  • Quantum Information & Computation
  • Year:
  • 2002

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Abstract

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 Möbius addition and scalar multiplication. The latter, in turn, form the algebraic setting for the Poincaré ball model of hyperbolic geometry so that, as a result, the qubit density matrix is linked to hyperbolic geometry.