Entanglement classification of three fermions with up to nine single-particle states

Gábor Sárosi and Péter Lévay
Phys. Rev. A 89, 042310 – Published 11 April 2014

Abstract

Based on results well known in the mathematics literature but not yet common knowledge in the physics literature, 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 stochastic local operations and classical communication (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 I6, I9, and I12 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.

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  • Received 17 December 2013

DOI:https://doi.org/10.1103/PhysRevA.89.042310

©2014 American Physical Society

Authors & Affiliations

Gábor Sárosi* and Péter Lévay

  • Department of Theoretical Physics, Institute of Physics, Budapest University of Technology and Economics, H-1521 Budapest, Hungary

  • *sarosi@phy.bme.hu
  • levay@phy.bme.hu

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Vol. 89, Iss. 4 — April 2014

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