Quantifying geometric measure of entanglement by mean value of spin and spin correlations with application to physical systems

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 spanned by vectors |↑↓⟩, |↓↑⟩ or |↑↑⟩, |↓↓⟩ is studied as well. The result are generalized for corresponding rank-2 mixed states of arbitrary N spin system. 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, Schrödinger cat in fluctuating magnetic field