Distilling entanglement from Fermions

TL;DR

This paper explores how to analyze and distill entanglement in Fermionic systems using algebraic methods, focusing on Gaussian states and applying the approach to free Fermions on a 1D lattice.

Contribution

It introduces an algebraic framework for studying Fermionic entanglement and distillation, especially for Gaussian states, diverging from traditional tensor product methods.

Findings

Develops an algebraic approach to Fermionic entanglement

Applies the scheme to Fermionic Gaussian states via covariance matrices

Demonstrates results with free Fermions on a 1D lattice

Abstract

Since Fermions are based on anti-commutation relations, their entanglement can not be studied in the usual way, such that the available theory has to be modified appropriately. Recent publications consider in particular the structure of separable and of maximally entangled states. In this talk we want to discuss local operations and entanglement distillation from bipartite, Fermionic systems. To this end we apply an algebraic point of view where algebras of local observables, rather than tensor product Hilbert spaces play the central role. We apply our scheme in particular to Fermionic Gaussian states where the whole discussion can be reduced to properties of the covariance matrix. Finally the results are demonstrated with free Fermions on an infinite, one-dimensional lattice.