  Quantum correlations in the state of four-level atom are investigated by
using generic unitary transforms of the classical (diagonal) density matrix.
Partial cases of pure state, $X$-state, Werner state are studied in details.
The geometrical meaning of unitary Hilbert reference-frame rotations generating
entanglement in the initially separable state is discussed. Characteristics of
the entanglement in terms of concurrence, entropy and negativity are obtained
as functions of the unitary matrix rotating the reference frame.
