Entanglement for multipartite systems of indistinguishable particles

TL;DR

This paper develops a unified framework for understanding entanglement in multipartite quantum systems with indistinguishable particles, using symmetry group representation theory and introducing a generalized S-rank to classify entanglement.

Contribution

It introduces a unified approach to entanglement in systems with arbitrary parastatistics, generalizing the Schmidt rank via S-rank and constructing analogs of the Jamiolkowski isomorphism for bosons and fermions.

Findings

Defined S-rank for all tensor types to distinguish pure state entanglement

Unified approach applicable to bosonic, fermionic, and parastatistical systems

Constructed analogs of the Jamiolkowski isomorphism for Bose and Fermi statistics

Abstract

We analyze the concept of entanglement for multipartite system with bosonic and fermionic constituents and its generalization to systems with arbitrary parastatistics. We use the representation theory of symmetry groups to formulate a unified approach to this problem in terms of simple tensors with appropriate symmetry. For an arbitrary parastatistics, we define the S-rank generalizing the notion of the Schmidt rank. The S-rank, defined for all types of tensors, serves for distinguishing entanglement of pure states. In addition, for Bose and Fermi statistics, we construct an analog of the Jamiolkowski isomorphism.