  The entanglement characteristics of two qubits are encoded in the invariants
of the adjoint action of SU(2) x SU(2) group on the space of density matrices
defined as the space of positive semi-definite Hermitian matrices. The
corresponding ring of polynomial invariants is studied. The special integrity
basis for this ring is described and constraints on its elements due to the
positive semi-definiteness of density matrices are given explicitly in the form
of polynomial inequalities. The suggested basis is characterized by the
property that only a minimal number of invariants, namely two primary
invariants of degree 2, 3 and one secondary invariant of degree 4 appearing in
the Hironaka decomposition of the ring are subject to the polynomial
inequalities.
