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Zapiski Nauchnykh Seminarov POMI, 2011, Volume 387, Pages 102–121 (Mi znsl4098)  
This article is cited in 3 scientific papers (total in 3 papers)

$\operatorname{SU}(6)$ Casimir invariants and $\operatorname{SU}(2)\otimes\operatorname{SU}(3)$ scalars for a mixed qubit-qutrit states

V. Gerdta, D. Mladenovb, Yu. Paliic, A. Khvedelidzed

a Laboratory of Information Technologies, Joint Institute for Nuclear Research, Dubna, Russia
b Department of Physics, Sofia State University, Sofia, Bulgaria
c Institute of Applied Physics, Chisinau, Moldova
d Department of Theoretical Physics, A. Razmadze Mathematical Institute, Tbilisi, Georgia
Full-text PDF (240 kB) Citations (3)
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Abstract: 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 $\mathfrak{su}(6)$.
Key words and phrases: entanglement, polynomial invariants, Molien function, positive definiteness.
Received: 20.11.2010
English version:
Journal of Mathematical Sciences (New York), 2011, Volume 179, Issue 6, Pages 690–701
DOI: https://doi.org/10.1007/s10958-011-0619-9
Bibliographic databases:
Document Type: Article
UDC: 517.986
Language: English
Citation: 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”, Representation theory, dynamical systems, combinatorial methods. Part XIX, Zap. Nauchn. Sem. POMI, 387, POMI, St. Petersburg, 2011, 102–121; J. Math. Sci. (N. Y.), 179:6 (2011), 690–701
Citation in format AMSBIB
\Bibitem{GerMlaPal11}
\by V.~Gerdt, D.~Mladenov, Yu.~Palii, A.~Khvedelidze
\paper $\operatorname{SU}(6)$ Casimir invariants and $\operatorname{SU}(2)\otimes\operatorname{SU}(3)$ scalars for a~mixed qubit-qutrit states
\inbook Representation theory, dynamical systems, combinatorial methods. Part~XIX
\serial Zap. Nauchn. Sem. POMI
\yr 2011
\vol 387
\pages 102--121
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl4098}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2011
\vol 179
\issue 6
\pages 690--701
\crossref{https://doi.org/10.1007/s10958-011-0619-9}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-83555165249}
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    • This publication is cited in the following 3 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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