We study the local quantum Fisher information (LQFI) in the mixed-spin Heisenberg XXZ chain. Both the maximal and minimal LQFI are studied and the former is essential to determine the accuracy of the quantum parameter estimation, the latter can be well used to characterize the discord-type quantum correlations. We investigate the effects of the temperature and the anisotropy parameter on the maximal LQFI and thus on the accuracy of the parameter estimation. Then we make use of the minimal LQFI to study the discord-type correlations of different site pairs. Different dimensions of the subsystems cause different values of the minimal LQFI which reflects the asymmetry of the discord-type correlation. In addition, the site pairs at different positions of the spin chains have different minimal LQFI, which reveals the influence of the surrounding spins on the bipartite quantum correlation. Our results show that the LQFI obtained through a simple calculation process provides a convenient way to investigate the discord-type correlation in high-dimensional systems.
We study the local quantum Fisher information (LQFI) in the mixed-spin Heisenberg XXZ chain. Both the maximal and minimal LQFI are studied and the former is essential to determine the accuracy of the quantum parameter estimation, the latter can be well used to characterize the discord-type quantum correlations. We investigate the effects of the temperature and the anisotropy parameter on the maximal LQFI and thus on the accuracy of the parameter estimation. Then we make use of the minimal LQFI to study the discord-type correlations of different site pairs. Different dimensions of the subsystems cause different values of the minimal LQFI which reflects the asymmetry of the discord-type correlation. In addition, the site pairs at different positions of the spin chains have different minimal LQFI, which reveals the influence of the surrounding spins on the bipartite quantum correlation. Our results show that the LQFI obtained through a simple calculation process provides a convenient way to investigate the discord-type correlation in high-dimensional systems.
Abstract Quantum correlations play an important role in quantum information theory. Quantum Fisher information (QFI) via local observables and via local measurements (i.e. local QFI (LQFI)) is a fundamental concept in quantum estimation and quantum metrology. LQFI captures the quantumness of correlations in a multicomponent quantum system. This new discord-like measure is very similar to the quantum correlations measure called local quantum uncertainty (LQU). In this work we will study the LQFI and the LQU in the two-qubit Heisenberg XYZ spin chain model with Dzyaloshinskii–Moriya (DM) interaction in the z -direction. Here we show that the DM interaction and spin interactions along the x - and z -axes can increase and maintain LQFI and LQU. It is also shown that because of thermal fluctuations LQFI and LQU are decreased by increasing temperature. They are equal to one at very low temperature and start to decay only after a thereshold temperature.
Abstract The thermal quantum correlations’ dynamics of an anisotropic two-qubit Heisenberg XYZ model in the presence of a x-projection external magnetic field are investigated in this paper. We use local quantum-Fisher information (LQFI), and log-negativity, and local quantum-uncertainty (LQU) to analyze the generated quantum correlation dynamics. Using the associated parameters, we demonstrate the successful generation of entanglement and quantum correlations beyond entanglement in the anisotropic spin-chain state. Certain values and ranges of anisotropy, external magnetic field, and spin coupling strength are proposed that can be used to achieve either a non-maximal or maximal quantum correlated state. The characterization of the spin-chain state by various parameters determines the dynamical patterns, degree, and preservation limits of the associated quantum correlations. Finally, the LQFI, LQU, and log-negativity functions’ robustness is highly dependent on their parameters, and they rarely agree on the degree of quantum correlations and dynamical patterns.
Abstract Many measures of quantum correlations have been introduced so far, and now their properties are carefully studied both theoretically and experimentally. The most important among them are quantum entanglement and quantum discord. Recently, it was shown that the Wigner–Yanase skew information and quantum Fisher information also can serve as measures of nonclassical correlations. These discordlike measures are called local quantum uncertainty (LQU) and interferometric power or local quantum Fisher information (LQFI), correspondingly. In this paper the behavior of LQU and LQFI is considered at thermal equilibrium of the two-qubit Heisenberg models in the absence and presence of an external magnetic field; these cases correspond to the Bell-diagonal and general X states, respectively.
Pairwise quantum discord (QD) and entanglement of the three-qubit XXZ Heisenberg spin chain with two types of three-site interactions and an external magnetic field are investigated. Our study found that both entanglement and quantum discord could detect the quantum critical phenomena of this model. We were able to obtain a nonzero value of quantum discord even at high temperature with the increase of XZX[Formula: see text]YZY or XZY[Formula: see text]YZX three-site interaction, however, the cooperative effect of XZX[Formula: see text]YZY and XZY[Formula: see text]YZX interactions is more ideal. Furthermore, in contrast to XZY[Formula: see text]YZX and XZX[Formula: see text]YZY interactions, the cooperative effect of XZX[Formula: see text]YZY and XZY[Formula: see text]YZX three-site interactions is more efficient to enhance the maximum value of quantum discord. Likewise, the cooperative effect of XZX[Formula: see text]YZY and XZY[Formula: see text]YZX interactions is the most optimal to increase the range of magnetic field or anisotropy parameter where quantum discord maintains the maximum value.
The quantum discord, which quantifies the amount of quantum correlation present between parts of a system, is investigated for spin systems. The discord for a pair of spins in the many-spin ground state, computed by minimizing the conditional entropy of the two spins, is related to the diagonal and off-diagonal spin–spin correlation functions and the local magnetization. We show that for isotropic and translationally invariant states, the discord depends only on the diagonal spin correlation function. Thus, near a thermal/quantum critical point, the pairwise discord exhibits long-range behavior, analogously to the correlation function. The discord exhibits a kink singularity as a function of the anisotropy parameter for the ground state of the anisotropic Heisenberg model, for both nearest-neighbor spins as well as for well-separated spins. The preferred measurement basis for the minimum conditional entropy, which determines the discord, changes discontinuously across the critical point. We also investigate, from exact numerical diagonalization, the distribution of conditional entropies as the measurement basis is varied. For the isotropic model, the conditional entropy distribution is a δ-function, whereas it has a twin-peak structure for the anisotropic model. It is shown that the average value and the mean-square fluctuation of the conditional entropy also show a signature of the critical-point behavior.
Abstract The thermal quantum correlations in a two-qubit one-dimensional XXZ Heisenberg spin- 1 2 chain subjected to an inhomogeneous magnetic field are investigated. The concurrence, as thermal entanglement quantifier, and the discord-like quantifiers, namely the trace distance discord and local quantum uncertainty, are computed. Their dependence on the anisotropy parameter γ , uniform magnetic field B , coupling constant J and nonuniform magnetic field b are presented in detail. The mentioned quantifiers behaviors in terms of this parameters are compared and discussed. The results show that TDD is always much stronger than the concurrence and LQU, whereas the latter two show a swinging behavior depending on system parameters. Also, we have shown that the nonuniform magnetic field can reduce the effects of temperature on thermal correlations. Furthermore, the thermal correlations, for fixed values of b , can be enhanced in the antiferromagnetic system in comparison to the ferromagnetic one. In addition, the quantum correlations amounts in the ferromagnetic system are deteriorated when γ decreases, but they are improved when the system is antiferromagnetic.