Quantifying geometric measure of entanglement by mean value of spin and spin correlations for pure and mixed states

TL;DR

This paper presents a method to quantify the geometric measure of entanglement using mean spin values and correlations, applicable to both pure and mixed quantum states, facilitating experimental measurement.

Contribution

It derives explicit relations between geometric entanglement and observable spin quantities for pure and mixed states, enabling experimental estimation of entanglement.

Findings

Explicit formulas for geometric entanglement in pure states using mean spin.

Relation of entanglement to spin correlations in mixed states of rank-2.

Application of results to entanglement dynamics in spin chains and magnetic fields.

Abstract

We quantify the geometric measure of entanglement in terms of mean values of observables of entangled system. For pure states we find the relation of geometric measure of entanglement with the mean value of spin one-half for the system composed of spin and arbitrary quantum system. The geometric measure of entanglement for mixed states of rank-2 is studied as well. We find the explicit expression for geometric entanglement and the relation of entanglement in this case with the values of spin correlations. These results allow to find experimentally the value of entanglement by measuring a value of the mean spin and the spin correlations for pure and mixed states, respectively. The obtained results are applied for calculation of entanglement during the evolution in spin chain with Ising interaction , two-spin Ising model in transverse fluctuating magnetic field, Schr\"odinger cat in fluctuating magnetic field.