Gábor Sárosi, Péter Lévay
Published 2013-12-10, updated 2014-04-16Version 2
Based on results well known in the mathematics literature but have not made their debut to the physics literature yet we conduct a study on three-fermionic systems with six, seven, eight and nine single-particle states. Via introducing special polynomial invariants playing the role of entanglement measures the structure of the SLOCC entanglement classes is investigated. The SLOCC classes of the six- and seven-dimensional cases can elegantly be described by special subconfigurations of the Fano plane. Some special embedded systems containing distinguishable constituents are arising naturally in our formalism, namely, three-qubits and three-qutrits. In particular the three fundamental invariants $I_6$, $I_9$, and $I_{12}$ of the three-qutrits system are shown to arise as special cases of the four fundamental invariants of three-fermions with nine single-particle states.
Comments: 56 pages, 3 figures. Changes made: We changed the title to be more informative and to meet the suggestion of the journal. We added a new section (Sec V.) on pinning of occupation numbers. We corrected some factors due to an unfortunate mismatch in the normalization convention in e.q. (149). We corrected some wrong factors in e.q. (176). We corrected several typos through the text
Journal: Phys. Rev. A 89, 042310 (2014)
Polynomial invariants of degree 4 for even-$n$ qubits and their applications in entanglement classification
Matrix Pencils and Entanglement Classification
Entanglement Classification of Restricted Greenberger-Horne-Zeilinger Symmetric States in Four-Qubit System
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