Quantum correlations in spin models

Abstract

Bell nonlocality, entanglement and nonclassical correlations are different aspects of quantum correlations for a given state. There are many methods to measure nonclassical correlations. In this paper, nonclassical correlations in two-qubit spin models are measured by use of measurement-induced disturbance (MID) [Phys. Rev. A, 77, 022301 (2008)] and geometric measure of quantum discord (GQD) [Phys. Rev. Lett. 105, 190502 (2010)]. Their dependencies on external magnetic field, spin-spin coupling, and Dzyaloshinski-Moriya (DM) interaction are presented in detail. We also compare Bell nonlocality, entanglement measured by concurrence, MID and GQD and illustrate their different characteristics.

Quantum discord and its allies: a review of recent progress

“…In particular, in Ref. [531], the XXZ model with an external field and the XXX model with DM interaction were considered, and the dependencies of GQD on the system parameters were studied. Similar work in this direction has also been reported by Cai et al [533] where the DM interaction has been included along with an XXZ interaction.…”

Comparative study of the geometric quantum discord in the transverse Ising model

“…Recently, quantum discord in various spin models have been studied by a number of authors [46][47][48][49][50][51][52][53][54][55][56]. Particularly, the spin-1/2 model with Ising interactions between neighbors has attracted wide attention due to its clear physical picture.…”

Maximum violation of Wigner inequality for two-spin entangled states with parallel and antiparallel polarizations

“…[10][11][12][13][14] Bell nonlocality and quantum entanglement in two-qubit spin model are also measured by use of measurement induced disturbance and quantum discord. 15 The experimental evidence [13][14][15][16][17][18][19][20][21] confirming the violation of BI provides an overwhelming superiority for the non-locality in quantum mechanics against the proposition of local realism. 22,23 In various modified forms of the BI, the Clauser-Horne-Shimony-Holt (CHSH) inequality 24 is of particular interesting to the experimental test, since it provides a quantitative bound of the four-direction measuring-outcome correlation P lc CHSH ≤ 2 for the local realist theory.…”