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arXiv:1301.5394 · Quantum Information Processing

Quantum discord in spin systems with dipole–dipole interaction

E. I. Kuznetsova, Mikhail A. Yurischev

Published Aug 8, 2013• 25 citations
arXivHTMLPDF
DOI
10.1007/s11128-013-0617-6

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We consider a spin ring with an arbitrary number of spins on the ring and one spin in its center in a strong external magnetic field.The spins on the ring are connected by the secular dipole-dipole interactions and interact with the central spin through the Heisenberg zz-interaction.We show that the quantum discord, describing quantum correlations between the ring and the central spin, can be obtained analytically for an arbitrary number of the spins in the high-temperature approximation.We demonstrate the evolution of quantum correlations at different numbers of the spins.The contributions of longitudinal and transversal spin interactions to the quantum discord are discussed.
It is known from the analysis of the density matrix for bipartite systems that the quantum discord (as a measure of quantum correlations) depends on the particular subsystem chosen for the projective measurements. We study asymmetry of the discord in a simple physical model of two spin-1/2 particles with the dipole-dipole interaction governed by the XY Hamiltonian in the inhomogeneous magnetic field. The dependence of the above discord asymmetry on the Larmor frequencies at both T = 0 (the ground state) and T > 0 has been investigated. It is demonstrated, in particular, that the asymmetry is negligible for high temperatures but it may become significant with a decrease in the temperature.