Geometric measure of pairwise quantum discord for superpositions of multipartite generalized coherent states

We give the explicit expressions of the pairwise quantum correlations present in superpositions of multipartite coherent states. A special attention is devoted to the evaluation of the geometric quantum discord. The dynamics of quantum correlations under a dephasing channel is analyzed. A comparison of geometric measure of quantum discord with that of concurrence shows that quantum discord in multipartite coherent states is more resilient to dissipative environments than is quantum entanglement. To illustrate our results, we consider some special superpositions of Weyl–Heisenberg, SU(2)$\mathit{SU}(2)$ and SU(1,1)$\mathit{SU}(1,1)$ coherent states which interpolate between Werner and Greenberger–Horne–Zeilinger states.     

The quantum correlation of anisotropic Heisenberg spin chain under the control of inhomogeneous magnetic field

The quantum correlation (quantum entanglement and quantum discord)’s dynamical behavior characteristics of Heisenberg XXZ spin chain with Dzyaloshinskii–Moriya (DM) interaction heterogeneous magnetic field that manipulated by sinusoidal wave are investigated in this paper. The results indicate that quantum correlation of anisotropic Heisenberg XXZ spin chain can be regulated effectively by magnetic field intensity B and magnetic field uniformity cos θ   of the external magnetic field. Under the effects of DM interaction in qubits, the quantum correlation's dynamics evolution process appears sudden death and birth. But DM interaction has a critical value D_CZ$D_{CZ}$ which is connected with other quantum correlation versus parameters. Only when Dz≥D_CZ$D_z\ge D_{CZ}$, sudden death and birth can be obviously observed under the rest given parameters.     

Remanent quantum correlations in dissipative qubits

Starting from the exact evolution of a Markovian dissipative quantum walk, a non-Markovian decoherence of two qubits interacting with a phonon thermal bath has been investigated analytically using quantum information tools. Concurrence and quantum discord are affected in a complex way, showing that entanglement decreases with dissipation. At the limit where dissipation dominates, quantum correlations survive in time as ∝t^−1/2$\propto t^{-1/2}$. Thus, even under the influence of dissipation, two qubits retain their quantumness for a long time. Quantum correlations could be therefore observed for a long time in related photonic experiments.     

Multipartite distribution property of one way discord beyond measurement

We investigate the distribution property of one way discord in the multipartite system by introducing the concept of polygamy deficit for one way discord. The difference between one way discord and quantum discord is analogue to the one between entanglement of assistance and entanglement of formation. For tripartite pure states, two kinds of polygamy deficits are presented with the equivalent expressions and physical interpretations regardless of measurement. For four-partite pure states, we provide a condition which makes one way discord polygamy satisfied. In addition, we generalize these results to the case for N$N$-partite pure states. Those results can be applicable to multipartite quantum systems and are complementary to our understanding of the shareability of quantum correlations.     

Deforming a Lie algebra by means of a 2-form

We consider a vector space V$V$ over K=R$\mathbb{K}=\mathbb{R}$ or C$\mathbb{C}$, equipped with a skew symmetric bracket [⋅,⋅]:V×V→V$[\cdot ,\cdot ]:V\times V\to V$ and a 2-form ω:V×V→K$\omega :V\times V\to \mathbb{K}$. A simple change of the Jacobi identity to the form [A,[B,C]]+[C,[A,B]]+[B,[C,A]]=ω(B,C)A+ω(A,B)C+ω(C,A)B$[A,[B,C]]+[C,[A,B]]+[B,[C,A]]=\omega (B,C)A+\omega (A,B)C+\omega (C,A)B$ opens up new possibilities, which shed new light on the Bianchi classification of three-dimensional Lie algebras.     

Qubit disentanglement in local squeezed reservoirs

We consider the influence of the local squeezed vacuum fields on two initially entangled two-qubit system. By considering the upper bound of entanglement under time evolution, we find that the decay of the quantum entanglement shows different behavior for different time scales (t?max{(2βA)⁻¹,(2βB)⁻¹}$t?\max \{{(2{\beta }_A)}^{\mathrm{-1}},{(2{\beta }_B)}^{\mathrm{-1}}\}$ and t?min{(2βA)⁻¹,(2βB)⁻¹}$t?\min \{{(2{\beta }_A)}^{\mathrm{-1}},{(2{\beta }_B)}^{\mathrm{-1}}\}$). The relative phase of the squeezing environment can also affect the entanglement dynamics profoundly.     

Non-extensive statistical entropy,quantum groups and quantum entanglement

In this work, we explore a new connection between quantum groups and Tsallis entropy through the energy spectrum of a Hamiltonian with S_Uq(2)$S{U}_q\left(2\right)$ symmetry. Identifying the deformation parameter of the entropy with the parameter of deformation of the associated quantum group, we deduce Tsallis entropy for states related to such a system with S_Uq(2)$S{U}_q\left(2\right)$ symmetry and conducted an investigation of quantum entanglement.     

DCCA cross-correlation coefficient differentiation: Theoretical and practical approaches

We propose in this paper to establish a well-defined relationship between _αDFA${\alpha }_{DFA}$ (the long range auto-correlation exponent) and _λDCCA${\lambda }_{DCCA}$ (the long range cross-correlation exponent), respectively described by the DFA and DCCA methods. This relationship will be accomplished theoretically by differentiating the DCCA cross-correlation coefficient, _ρDCCA(n)${\rho }_{DCCA}\left(n\right)$. Also, for some specific times series, we apply this theory in order to establish its validity.     

Oscillation of the NCO model

We study opinion oscillation of the nonconsensus opinion model (NCO) on graphs, and in particular on bipartite graphs. Using intensive numerical simulations, we investigate the relationship between amplitude A$A$ (the percentage of nodes whose opinions oscillate) and (p,q)$(p,q)$, which are the initial configuration fractions with opinion 1 on two sets of two bipartite graphs. Finally, for the general graph, we present several definitions and develop three propositions as regards whether an oscillation can occur or not on a certain graph.     

Integration over the Pauli quantum group

We prove that the Pauli representation of the quantum permutation algebra _As(4)$A_s\left(4\right)$ is faithful. This provides the second known model for a free quantum algebra. We use this model for performing some computations and show that, at the level of the laws of diagonal coordinates, the Lebesgue measure appears between the Dirac mass and the free Poisson law.     

Critical behavior and phase diagrams of a spin-1 Blume–Capel model with random crystal field interactions: An effective field theory analysis

A spin-1 Blume–Capel model with dilute and random crystal fields is examined for honeycomb and square lattices by introducing an effective-field approximation that takes into account the correlations between different spins that emerge when expanding the identities. For dilute crystal fields, we have given a detailed exploration of the global phase diagrams of the system in _kBTc/J−D/J$k_B{T}_c/J-D/J$ plane with the second and first order transitions, as well as tricritical points. We have also investigated the effect of the random crystal field distribution characterized by two crystal field parameters D/J$D/J$ and △/J$△/J$ on the phase diagrams of the system. The system exhibits clear distinctions in a qualitative manner with coordination number q$q$ for random crystal fields with △/J,D/J≠0$△/J,D/J\ne 0$. We have also found that, under certain conditions, the system may exhibit a number of interesting and unusual phenomena, such as reentrant behavior of first and second order, as well as a double reentrance with three successive phase transitions.     

Steering Witness and Steering Criterion of Gaussian States

Quantum steering is an important quantum resource, which is intermediate between entanglement and Bell nonlocality. In this paper, we study steering witnesses for Gaussian states in continuous-variable systems. We give a definition of steering witnesses by covariance matrices of Gaussian states, and then obtain a steering criterion by steering witnesses to detect steerability of any (m+n)-mode Gaussian states. In addition, the conditions for two steering witnesses to be comparable and the optimality of steering witnesses are also discussed.     

The anisotropic quantum spin-1/2 Heisenberg antiferromagnet in the presence of a longitudinal field on a bcc lattice

In this work we study the critical behavior of the quantum spin-1/2 anisotropic Heisenberg antiferromagnet in the presence of a longitudinal field on a body centered cubic (bcc) lattice as a function of temperature, anisotropy parameter (Δ)$(\Delta )$ and magnetic field (H  ), where Δ=0$\Delta =0$ and 1 correspond the isotropic Heisenberg and Ising models, respectively. We use the framework of the differential operator technique in the effective-field theory with finite cluster of N  =4 spins (EFT-4). The staggered _ms=(_mA−_mB)/2$m_s=(m_A-m_B)/2$ and total m=(_mA+_mB)/2$m=(m_A+m_B)/2$ magnetizations are numerically calculated, where in the limit of _ms→0$m_s\to 0$ the critical line _TN(H,Δ)$T_N(H,\Delta )$ is obtained. The phase diagram in the T−H$T-H$ plane is discussed as a function of the parameter Δ$\Delta$ for all values of H∈[0,_Hc(Δ)]$H\in [0,H_c(\Delta )]$, where _Hc(Δ)$H_c(\Delta )$ correspond the critical field (_TN=0)$(T_N=0)$. Special focus is given in the low temperature region, where a reentrant behavior is observed around of H=_Hc(Δ)≥_Hc(Δ=1)=8J$H=H_c(\Delta )\ge H_c(\Delta =1)=8J$ in the Ising limit, results in accordance with Monte Carlo simulation, and also was observed for all values of Δ∈[0,1]$\Delta \in [\mathrm{0,1}]$. This reentrant behavior increases with increase of the anisotropy parameter Δ$\Delta$. In the limit of low field, our results for the Heisenberg limit are compared with series expansion values.