Special entangled quantum systems and the Freudenthal construction

TL;DR

This paper introduces a new approach to quantifying entanglement in mixed quantum systems with distinguishable and identical particles using the Freudenthal construction, providing explicit classifications and measures.

Contribution

It demonstrates how the Freudenthal construction based on cubic Jordan algebras defines invariant entanglement measures and classifies SLOCC classes for these systems.

Findings

Explicit SLOCC class descriptions for multipartite entanglement.

Construction of multiqubit entanglement measures via embedding.

Plucker relations as criteria for separability.

Abstract

We consider special quantum systems containing both distinguishable and identical constituents. It is shown that for these systems the Freudenthal construction based on cubic Jordan algebras naturally defines entanglement measures invariant under the group of stochastic local operations and classical communication (SLOCC). For this type of multipartite entanglement the SLOCC classes can be explicitly given. These results enable further explicit constructions of multiqubit entanglement measures for distinguishable constituents by embedding them into identical fermionic ones. We also prove that the Plucker relations for the embedding system provide a sufficient and necessary condition for the separability of the embedded one. We argue that this embedding procedure can be regarded as a convenient representation for quantum systems of particles which are really indistinguishable but for some reason they are not in the same state of some inner degree of freedom.