Entanglement, Particle Identity and the GNS Construction: A Unifying Approach

TL;DR

This paper introduces a unified GNS-based framework for understanding entanglement that treats states and observables equally, effectively handling systems of identical particles and anyons beyond traditional methods.

Contribution

It presents a novel GNS construction approach that generalizes entanglement analysis, overcoming limitations of partial trace methods for identical particles and extending to exotic statistics.

Findings

Reproduces standard bipartite entanglement results

Overcomes limitations for identical particle systems

Applicable to anyons and para-statistics

Abstract

A novel approach to entanglement, based on the Gelfand-Naimark-Segal (GNS) construction, is introduced. It considers states as well as algebras of observables on an equal footing. The conventional approach to the emergence of mixed from pure ones based on taking partial traces is replaced by the more general notion of the restriction of a state to a subalgebra. For bipartite systems of nonidentical particles, this approach reproduces the standard results. But it also very naturally overcomes the limitations of the usual treatment of systems of identical particles. This GNS approach seems very general and can be applied for example to systems obeying para- and braid- statistics including anyons.