A universal framework for entanglement detection

TL;DR

This paper introduces a universal framework for detecting entanglement across different quantum particle types, providing a comprehensive set of measures with proven criteria for pure states and bounds for mixed states.

Contribution

It develops a unified approach to entanglement detection applicable to distinguishable particles, bosons, and fermions, linking measures to symmetry group representations and extending to mixed states.

Findings

Entanglement measures relate to symmetry group decompositions.

The criterion is necessary and sufficient for pure states.

Provides a lower bound for mixed state entanglement measures.

Abstract

We construct nonlinear multiparty entanglement measures for distinguishable particles, bosons and fermions. In each case properties of an entanglement measures are related to the decomposition of the suitably chosen representation of the relevant symmetry group onto irreducible components. In the case of distinguishable particles considered entanglement measure reduces to the well-known many particle concurrence. We prove that our entanglement criterion is sufficient and necessary for pure states living in both finite and infinite dimensional spaces. We generalize our entanglement measures to mixed states by the convex roof extension and give a non trivial lower bound of thus obtained generalized concurrence.