  Just as any state of a single qubit or 2-level system can be obtained from
any other state by a rotation operator parametrized by three real Euler angles,
we show how any state of an n-qubit or 2^n-level system can be obtained from
any other by a compact unitary transformation with 2^(n+1)-1 real angles, 2^n
of which are azimuthal-like and the rest polar-like. The results follow from a
modeling of the Hilbert space of n-qubits by a minimal left ideal of an
associative algebra. This representation is expected to be useful in the design
of new compact control techniques or more efficient algorithms in quantum
computing.
