  We discuss a generalization to 2 qubits of the standard Bloch sphere
representation for a single qubit, in the framework of Hopf fibrations of high
dimensional spheres by lower dimensional spheres. The single qubit Hilbert
space is the 3-dimensional sphere S3. The S2 base space of a suitably oriented
S3 Hopf fibration is nothing but the Bloch sphere, while the circular fibres
represent the qubit overall phase degree of freedom. For the two qubits case,
the Hilbert space is a 7-dimensional sphere S7, which also allows for a Hopf
fibration, with S3 fibres and a S4 base. A main striking result is that
suitably oriented S7 Hopf fibrations are entanglement sensitive. The relation
with the standard Schmidt decomposition is also discussed

Quantum Physics;Condensed Matter