Three fermions with six single particle states can be entangled in two inequivalent ways

Details Three fermions with six single particle states can be entangled in two inequivalent ways Three fermions with six single particle states can be entangled in two inequivalent ways

2008-06-25

arxiv.org/abs/0806.4076v1

Physical Review A78, 022329 (2008)

Physics

Quantum Physics

23 pages LATEX

Scientific paper

10.1103/PhysRevA.78.022329

Using a generalization of Cayley's hyperdeterminant as a new measure of tripartite fermionic entanglement we obtain the SLOCC classification of three-fermion systems with six single particle states. A special subclass of such three-fermion systems is shown to have the same properties as the well-known three-qubit ones. Our results can be presented in a unified way using Freudenthal triple systems based on cubic Jordan algebras. For systems with an arbitrary number of fermions and single particle states we propose the Pl\"ucker relations as a sufficient and necessary condition of separability.

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