The Hilbert-Schmidt norm as a measure of entanglement in spin-1/2 Heisenberg chain: generalized Bell inequality and distance between states

TL;DR

This paper demonstrates that the Hilbert-Schmidt norm can serve as a unified measure of entanglement in spin-1/2 Heisenberg chains, linking generalized Bell inequalities and state distances.

Contribution

It establishes the equivalence of entanglement measures based on Bell inequalities and state distances using the Hilbert-Schmidt norm for specific quantum systems.

Findings

Hilbert-Schmidt norm coincides with Bell inequality-based entanglement measure

Results apply to spin-1/2 Heisenberg chains with nearest-neighbor interactions

Provides a unified framework for entanglement quantification

Abstract

In this letter, we show that the measure of entanglement using the generalized Bell inequality and the distance between states coincide when we use the Hilbert-Schmidt norm. Our conclusions apply to the spin-1/2 Heisenberg chains with interaction between the first neighbors.