Spins extracted from fermionic states and their entanglement properties

TL;DR

This paper explores how extracting electrons from fermionic states yields spin states with various entanglement properties, analyzed through reduced density matrices and spin squeezing inequalities.

Contribution

It introduces a method to derive and analyze the entanglement of spin states obtained from fermionic systems using extraction modes and reduced density matrices.

Findings

Extracted spin states exhibit different forms of entanglement.

Spin squeezing inequalities can detect the entanglement.

Derived explicit expressions for n-body reduced density matrices.

Abstract

We investigate the spin states obtained by extracting $n$ electrons from closed-shell fermionic states. A partition of the system is defined through the introduction of the extraction modes. We derive the expression of the $n$-body reduced density matrices, which represent the extracted spin states. We show that these states exhibit different forms of spin entanglement, whose detection is discussed in terms of the spin squeezing inequalities.