Spin-spin interaction in the bulk of topological insulators

We apply mean-field theory and Hirsch-Fye quantum Monte Carlo method to study the spin-spin interaction in the bulk of three-dimensional topological insulators. We find that the spin-spin interaction has three different components: the longitudinal, the transverse and the transverse Dzyaloshinskii-Moriya-like terms. When the Fermi energy is located in the bulk gap of topological insulators, the spin-spin interaction decays exponentially due to Bloembergen-Rowland interaction. The longitudinal correlation is antiferromagnetic and the transverse correlations are ferromagnetic. When the chemical potential is in the conduction or valence band, the spin-spin interaction follows power law decay, and isotropic ferromagnetic interaction dominates in short separation limit.Comment: 9 pages, 10 figure

Assisted optimal state discrimination without entanglement

A fundamental problem in quantum information is to explore the roles of different quantum correlations in a quantum information procedure. Recent work [Phys. Rev. Lett., 107 (2011) 080401] shows that the protocol for assisted optimal state discrimination (AOSD) may be implemented successfully without entanglement, but with another correlation, quantum dissonance. However, both the original work and the extension to discrimination of $d$ states [Phys. Rev. A, 85 (2012) 022328] have only proved that entanglement can be absent in the case with equal a \emph{priori} probabilities. By improving the protocol in [Sci. Rep., 3 (2013) 2134], we investigate this topic in a simple case to discriminate three nonorthogonal states of a qutrit, with positive real overlaps. In our procedure, the entanglement between the qutrit and an auxiliary qubit is found to be completely unnecessary. This result shows that the quantum dissonance may play as a key role in optimal state discrimination assisted by a qubit for more general cases.Comment: 6 pages, 3 figures. Accepted by EPL. We extended the protocol for assisted optimal state discrimination to the case with positive real overlaps, and presented a proof for the absence of entanglemen