We review the concepts of quantum entanglement and quantum discord and present the entropic measures for these information correlations. We further provide examples demonstrating the presence of quantum information correlations in different paramagnetic materials with ferro- and antiferromagnetic coupling. The temperature behavior of the discord for atomic nuclear spins and decoherence of quantum states with electron and nuclear spins is discussed.

The total quantum correlation (discord) in Heisenberg dimers is expressed via the spin-spin correlation function, internal energy, specific heat or magnetic susceptibility. This allows one to indirectly measure the discord through neutron scattering, as well as calorimetric or magnetometric experiments. Using the available experimental data, we found the discord for a number of binuclear Heisenberg substances with both antiferro- and ferromagnetic interactions. For the dimerized antiferromagnet copper nitrate Cu(NO_3)_2*2.5H_2O, the three independent experimental methods named above lead to a discord of approximately 0.2-0.3 bit/dimer at a temperature of 4 K. We also determined the temperature behavior of discord for hydrated and anhydrous copper acetates, as well as for the ferromagnetic binuclear copper acetate complex [Cu_2L(OAc)]*6H_2O, where L is a ligand.Comment: 7 pages, 6 figure

Entanglement and quantum discord for a pair of nuclear spins s = 1/2 in a nanopore filled with a gas of spin-carrying molecules (atoms) are studied. The correlation functions describing dynamics of dipolar coupled spins in a nanopore are found. The dependence of spin-pair entanglement on the temperature and the number of spins is obtained from the reduced density matrix, which is centrosymmetric (CS). An analytic expression for the concurrence is obtained for an arbitrary CS density matrix. It is shown that the quantum discord as a measure of quantum correlations attains a significant value at low temperatures. It is shown also that the discord in the considered model has "flickering" character and disappears periodically in the course of the time evolution of the system. The geometric discord is studied for arbitrary 4 × 4 CS density matrices.

Recent magnetic susceptibility measurements for polycrystalline samples of binuclear nitrosyl iron complexes, [Fe 2 (C 3 H 3 N 2 S) 2 (NO) 4 ] (I) and [Fe 2 (SC 3 H 5 N 2 ) 2 (NO) 4 ] (II), suggest that quantum-mechanical entanglement of the spin degrees of freedom exists in these compounds. Entanglement E exists below the temperature T E that we have estimated for complexes I and II to be 80-90 and 110-120 K, respectively. Using an expression of entanglement in terms of magnetic susceptibility for a Heisenberg dimer, we find the temperature dependence of the entanglement for complex II. Having arisen at the temperature T E , the entanglement increases monotonically with decreasing temperature and reaches 90-95% in this complex at T = 25 K, when the side effects are still small.

Previously [22], we made an attempt to theoreti cally study the dynamical quantum correlations in a model of N moving I = 1/2 spins confined in the pres ence of a strong magnetic field B 0 in a volume with an Abstract-A local orthogonal transformation that transforms any centrosymmetric density matrix of a two qubit system to the X form has been found. A piecewise analytic-numerical formula Q = min{Q π/2 , Q θ , Q 0 }, where Q π/2 and Q 0 are analytical expressions and the branch Q θ can be obtained only by numerically searching for the optimal measurement angle θ ∈ (0, π/2), is proposed to calculate the quantum discord Q of a general X state. The developed approaches have been applied for a quantitative description of the recently predicted flickering (periodic disappearance and reappearance) of the quantum information pair correlation between nuclear 1/2 spins of atoms or molecules of a gas (for example, 129 Xe) in a bounded volume in the presence of a strong magnetic field.

It is emphasized that quantum entanglement determined in terms of the von Neumann entropy operator is a stochastic quantity and, therefore, can fluctuate. The rms fluctuations of the entanglement entropy of two qubit systems in both pure and mixed states have been obtained. It has been found that entanglement fluctu ations in the maximally entangled states are absent. Regions where the entanglement fluctuations are larger than the entanglement itself (strong fluctuation regions) have been revealed. It has been found that the mag nitude of the relative entanglement fluctuations is divergent at the points of the transition of systems from an entangled state to a separable state. It has been shown that entanglement fluctuations vanish in the separable states.

Experimental results of multifrequency HF Doppler radar studies during electromagnetic pumping of the ionosphere from the ground are reported. The Doppler shifts of the radar waves after turn-on of the vertically injected HF pump wave depend on the pump frequency and exhibit, at relatively large reflection altitudes, opposite signs for pump frequencies above or below an electron gyroharmonic. The results are interpreted in terms of pump-induced plasma expulsion and enhanced ionization. For pump frequencies at a gyroharmonic, a minimum of plasma perturbation is detected with the radars. [S0031-9007(96)02265-X] PACS numbers: 94.20.Bb, 52.25.Sw, 52.35.Mw, 94.20.Tt

For the fully anisotropic simple-cubic Ising lattice, the critical finite-size scaling amplitudes of both the spin-spin and energy-energy inverse correlation lengths and the singular part of the reduced free-energy density are calculated by the transfer-matrix method and a finite-size scaling for cyclic L × L × ∞ clusters with L = 3 and 4. Analysis of the data obtained shows that the ratios and the directional geometric means of above amplitudes are universal.