Visnyk of the Lviv University. Series Physics 56 (2019) . 56-64
DOI: https://doi.org/10.30970/vph.56.2019.56

Entanglement of spins in triangle spin cluster

Yu. Z. Golskyi, Kh. P. Gnatenko

Entanglement is a prominent quantum phenomenon. Quantification of entanglement is important problem in quantum information theory. We study the geometric measure of entanglement which is defined as a minimal squared distance between an entangled state and separable states and is one of the widely used measures of entanglement. Recently, the authors of the paper [A. M. Frydryszak, M. I. Samar, V. M. Tkachuk Eur. Phys. J. D 71, 233, 2017] showed that the geometric measure of entanglement of a spin with arbitrary quantum system is related with observable values. Namely, they found relation of the geometric measure entanglement of a spin with its mean value. This relation opens possibility to find the geometric measure entanglement experimentally. We apply this result to the case of system of three spins, triangle spin cluster, which is described by Hamiltonian HT=-J(\sigmaz0\sigmaz1+\sigmaz1\sigmaz2+\sigmaz2\sigmaz0)-h(\sigmaz0+\sigmaz1+\sigmaz2), where \sigmazi are Pauli operators for spin i, J, h are constants which describe the interaction and the magnetic field, respectively. It is important to note that this spin model can be realized in the experiment. It describes spins in molecular cluster of dysprosium. We calculate geometric measure of entanglement of spins in the triangle spin cluster on the basis of the relation of the entanglement of the spin with its mean value. We find that the entanglement of a spin in the triangle spin cluster with other spins is determined by the mean values of spins in the initial state and the values of interaction J. This result opens possibility to find experimentally the value of entanglement of spins in the triangle spin cluster by measuring the mean values of spins.

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