Spin correlations and entanglement in partially magnetised ensembles of fermions

TL;DR

This paper establishes bounds on entanglement in fermionic spin ensembles using measurable quantities like singlet fraction and magnetization, providing a practical entanglement witness applicable to experiments.

Contribution

It introduces a tight, assumption-free criterion relating singlet fraction and magnetization to bipartite entanglement in fermions, enabling experimental detection.

Findings

Derived a bound for bipartite entanglement based on singlet fraction and magnetization.

Proved the condition $p_s > (1-m^2)/2$ as a sufficient entanglement witness.

Discussed implications for experiments and entanglement dynamics in cold Fermi gases.

Abstract

We show that the singlet fraction $p_s$ and total magnetisation (or polarisation) $m$ can bound the minimum concurrence in an ensemble of spins. We identify $p_s > (1-m^2)/2$ as a sufficient and tight condition for bipartite entanglement. Our proof makes no assumptions about the state of the system or symmetry of the particles, and can therefore be used as a witness for spin entanglement between fermions. We discuss the implications for recent experiments in which spin correlations were observed, and the prospect to study entanglement dynamics in the demagnetisation of a cold Fermi gas.