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

the european physical journal. d, atomic, molecular and optical physics/the european physical journal. d, atomic, molecular, optical and plasma physics

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