We study the validity of quantum Fisher information (QFI) as a faithful quantum coherence and correlation quantier by drawing a comparison with subsystem's coherence measure, rst-order coherence (FOC) and the entanglement measure, Negativity to study the behavior of thermal quantum coherence and correlations in two qubit Heisenberg XXX model, placed in independently controllable magnetic eld by systematically varying the coupling parameter, magnetic eld and bath temperature for ferromagnetic and antiferromagnetic case. After carefully observing the prole of quantum coherence and correlation measures, we propose an inequality relations which shows that there may exist a quantitative relationship between QFI, Negativity and FOC in which, the equality exists at zero temperature. We identify QFI to be a more useful coherence quantier, as it quanties coherence of individual subsystems and correlations among the subsystems. On the other hand, FOC identies coherence present in the individual subsystems only. A reciprocal relationship between Negativity and FOC is also observed in dierent cases. We also observe the existence of entanglement in ferromagnetic case, in contrast to simple Heisenberg XXX model in uniform magnetic eld. We show that in the ferromagnetic case, a very small inhomogeneity in magnetic eld is capable of producing large values of thermal entanglement. This shows that the behavior of entanglement in the ferromagnetic Heisenberg system is highly unstable against inhomogeneity of magnetic elds, which is inevitably present in any solid state realization of qubits.
We study the validity of quantum Fisher information (QFI) as a faithful quantum coherence and correlation quantier by drawing a comparison with subsystem's coherence measure, rst-order coherence (FOC) and the entanglement measure, Negativity to study the behavior of thermal quantum coherence and correlations in two qubit Heisenberg XXX model, placed in independently controllable magnetic eld by systematically varying the coupling parameter, magnetic eld and bath temperature for ferromagnetic and antiferromagnetic case. After carefully observing the prole of quantum coherence and correlation measures, we propose an inequality relations which shows that there may exist a quantitative relationship between QFI, Negativity and FOC in which, the equality exists at zero temperature. We identify QFI to be a more useful coherence quantier, as it quanties coherence of individual subsystems and correlations among the subsystems. On the other hand, FOC identies coherence present in the individual subsystems only. A reciprocal relationship between Negativity and FOC is also observed in dierent cases. We also observe the existence of entanglement in ferromagnetic case, in contrast to simple Heisenberg XXX model in uniform magnetic eld. We show that in the ferromagnetic case, a very small inhomogeneity in magnetic eld is capable of producing large values of thermal entanglement. This shows that the behavior of entanglement in the ferromagnetic Heisenberg system is highly unstable against inhomogeneity of magnetic elds, which is inevitably present in any solid state realization of qubits.
We investigate the behavior of thermal quantum coherence in the Heisenberg XXX model for a two-qubit system placed in independently controllable Inhomogeneous magnetic fields applied to two qubits respectively. We discuss the behavior of quantum coherence by systematically varying the coupling parameter, magnetic field, and temperature for both ferromagnetic and antiferromagnetic cases. The results show the interesting behavior of quantum coherence in a certain range of parameters. Generally, it is observed that quantum correlations decay with temperature, but in the ferromagnetic case with uniform magnetic interaction, it rises with temperature up to a certain threshold value and ultimately it decreases its value to zero. Moreover, it is observed that preserving the quantum coherence for small temperatures is very hard with the increasing magnetic field because, at small temperatures, quantum coherence decays sharply with the increase in magnetic field whereas at larger temperatures it decays completely at fairly large values of the magnetic field. The variation of quantum coherence with uniform magnetic field in the antiferromagnetic case is observed to be Gaussian for larger temperature but at zero or nearly zero temperature, it behaves as a constant function for uniform magnetic field up to a threshold value and then decays to zero with an infinite slope. This shows the signature of quantum phase transition from quantum nature to classicality.
Abstract We employ entanglement negativity, local quantum uncertainty (LQU), and local quantum Fisher information (LQFI) to characterize thermal entanglement between two XYZ-Heisenberg-qubit states under the influence of Dzyaloshinsky-Moriya(DM) and Kaplan-Shekhtman-Entin-Wohlman-Aharony (KSEA) interactions, as well as a magnetic field and thermal equilibrium temperature. A comparative examination reveals similar behaviors among these correlation measures. For the antiferromagnetic scenario, we observe that increasing the DM interaction parameter D z enhances thermal entanglement. Conversely, in the ferromagnetic case, the behavior of thermal entanglement differs with varying D z . Additionally, employing Kraus operators, we explore the performance of these quantifiers under decoherence. Notably, LQFI exhibits greater robustness than negativity and LQU, even displaying a frozen phenomenon at some time under dephasing effects.
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.
Thermal entanglement of spins are investigated in the several Heisenberg models by using of various entanglement measures, and we will evaluate the quantity of thermal entanglement with different parameters of the system (such as, magnetic field, temperture, impurity and different components of interaction). In part of proceduring, we will show that entanglement between two spins have a gaussian profile at the low temperature, and we show that there exists a relation between the QPT and the entanglement in three – qubit Heisenberg chain under the effect of impurity. In fact, QPT is the structure change in property of the ground state at the many–body system, which occures at absolute zero temperature and is purely driven by quantum fluctuation. This transitions appear with the change of a physical parameter. Thus we expect that phase transitions and critical behavior of systems can be explained by entanglement. Also, we investigate the entanglement in pure and thermal cluster states and pay attention to entanglement generation from thermal spin states inputed in a beam spliter. Then, thermal entanglement of Bosonic atoms are investigated in an optical lattices with nonlinear couplings and inhomogeneous magnetic field parameters by using of Negativity measure. We understand from the receiving results that nonlinear coupling coefficient support to entanglement can be improve under antiparalel magnetic field. Finally, we investigate quantum Teleportation at the Heisenberg model in presence of system impurity, as the result of quantum entanglement. We will demonstrate that the Fidelity average, as the measure for evaluation quantum Teleportation, can be controled by modulating magnetic field and impurity parameter
Keywords:
Beam Spliter, Closest Separable State, Concurrence, Entanglement, Fidelity Average, Generation Entanglement, Ground State Entanglement, Heisenberg Model, Impurity, Inhomogenous, Negativity, Nonlinear Coupling, Normal Lattice, Pure Cluster States, Pure state, Quantum Phase Transition, Quantum Teleportation, Thermal Entanglement.
In this paper, we investigate the pairwise quantum correlations in a two-qubit anisotropic Heisenberg model under the interplay of Calogero–Moser (CM) and Dzyaloshinsky–Moriya (DM) interactions in the presence of the homogeneous and inhomogeneous magnetic fields. We employ, respectively, the logarithmic negativity and local quantum uncertainty (LQU) to characterize the degree of entanglement and the amount of quantum correlations between the two parties of the considered system in equilibrium with a thermal reservoir. We analyze and compare the behaviors of the two quantum correlation quantifiers in the thermal state of the chain spin system and we discuss how relative distance between spins, equilibrium temperature, DM interaction coupling parameter and the external magnetic fields strengths influence the variations of both quantum correlation measures in such system.
Abstract In this study, we use the concept of l 1-norm coherence to characterize the entanglement of a two–qutrit Heisenberg XXZ model for subject to a uniform magnetic field and z–axis Dzyaloshinskii–Moriya interaction with Herring-Flicker coupling. We show that the temperature, magnetic field, DM interaction, and distance of Herring-Flicker coupling can all control the entanglement. However, the state system becomes less entangled at high temperatures or strong magnetic fields and vice versa. Our findings suggest that entanglement rises when the z–axis DM interaction increases. Additionally, we show that plateau behavior in the entanglement between spins (1, 1) occurs in the XXZ Heisenberg spin system and is influenced by the magnetic field, demonstrating that thermal agitation can weaken entanglement plateaus. Moreover, by setting the strengths coupling of the spin, we quickly recover the isotropic XY and XXX Heisenberg models. Finally, Herring-Flicker coupling affects the degree of entanglement. When Herring-Flicker coupling and temperature are at small values, the degree of entanglement is at its highest. Still, when Herring-Flicker coupling is at substantial values, the degree of entanglement tends to stabilize.