Geodesic
$\operatorname{SU}(6)$ Casimir invariants and $\operatorname{SU}(2)\otimes\operatorname{SU}(3)$ scalars for a~mixed qubit-qutrit states
Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems, combinatorial methods. Part XIX, Tome 387 (2011), pp. 102-121

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In the present paper few steps are undertaken towards the description of the “qubit-qutrit” pair – 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 positive semi-definiteness of the density operator is formulated explicitly as a set of inequalities in five Casimir invariants of the enveloping algebra $\mathfrak{su}(6)$. 
@article{ZNSL_2011_387_a3,
     author = {V. Gerdt and D. Mladenov and Yu. Palii and A. Khvedelidze},
     title = {$\operatorname{SU}(6)$ {Casimir} invariants and $\operatorname{SU}(2)\otimes\operatorname{SU}(3)$ scalars for a~mixed qubit-qutrit states},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {102--121},
     publisher = {mathdoc},
     volume = {387},
     year = {2011},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2011_387_a3/}
}
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V. Gerdt; D. Mladenov; Yu. Palii; A. Khvedelidze. $\operatorname{SU}(6)$ Casimir invariants and $\operatorname{SU}(2)\otimes\operatorname{SU}(3)$ scalars for a~mixed qubit-qutrit states. Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems, combinatorial methods. Part XIX, Tome 387 (2011), pp. 102-121. http://geodesic.mathdoc.fr/item/ZNSL_2011_387_a3/