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 Poincaré 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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Published in Zapiski Nauchnykh Seminarov POMI, Vol. 387, 2011, pp. 102–121.
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Gerdt, V., Mladenov, D., Palii, Y. et al. SU(6) Casimir invariants and SU(2) ⊗ SU(3) scalars for a mixed qubit-qutrit state. J Math Sci 179, 690–701 (2011). https://doi.org/10.1007/s10958-011-0619-9
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DOI: https://doi.org/10.1007/s10958-011-0619-9