Abstract
In the present paper, a few steps are undertaken towards the description of the “qubit–qutrit” pair – a quantum bipartite system composed of two- and three-level subsystems. Calculations of the Molien functions and Poincare series for the qubit-qubit and qubit-qutrit “local unitary invariants” are outlined and compared with the known results. The requirement of the positive semi-definiteness of the density operator is formulated explicitly as a set of inequalities in five Casimir invariants of the enveloping algebra $ \mathfrak{su}$ (6). Bibliography: 26 titles.
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