Entanglement and Hilbert space geometry for systems with a few qubits

摘要

This paper reviews recent attempts to describe the two- and three-qubit Hilbert space geometries. In the first part, this is done with the help of Hopf fibrations of hyperspheres. It is shown that the associated Hopf map is strongly sensitive to states' entanglement content. In the two-qubit case, a generalisation of the celebrated one-qubit Bloch sphere representation is described. In the second part, we present Hilbert space discrete versions, which are comparable to polyhedral approximations of spheres in standard geometry.