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

Entanglement calculations have received renewed interest with the advances observed in the field of quantum computing. Alternative methods to calculate entanglement that can be applied to broader classes of problems have become increasingly necessary. 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 the interaction between the first neighbours.