Abstract
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 to use the Plücker relations as a sufficient and necessary condition of separability.
- Received 25 June 2008
DOI:https://doi.org/10.1103/PhysRevA.78.022329
©2008 American Physical Society