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Physica Scripta

Thermal local Fisher information and quantum uncertainty in Heisenberg model

A-B A Mohamed, Hichem Eleuch

Published Aug 11, 2022• 11 citations
Publisher

Abstract

Abstract This study explores the spontaneous emergence of local Fisher information and local quantum uncertainty beyond entanglement in a noisy two-qubit Heisenberg XXX model with Dzyaloshinskii-Moria (DM) and Kaplan-Shekhtman-Entin-Wohlman-Aharony (KSEA) interactions. Local quantum Fisher information, local quantum uncertainty, and logarithmic negativity are used to examine two-spin non-locality. We find that by employing strong two-spin, Dzyaloshinskii- Moriya, and Kaplan-Shekhtman-Entin-Wohlman-Aharony interactions, we can prevent noise-induced losses in local Fisher information, local quantum uncertainty, and logarithmic negativity. The robustness of the two-spin non-localities is greater for a strong spin’s coupling strength than for the strong DM and KSEA interactions. Local Fisher information and local quantum uncertainty, as well as logarithmic-negativity, display asymmetric behaviors with respect to two-spin coupling and symmetric behaviors with respect to the Dzyaloshinskii-Moriya and Kaplan-Shekhtman-Entin-Wohlman-Aharony interactions. At high bath temperatures, the phenomenon of sudden-death two-spin entanglement emerges. Furthermore, by combining the parameters of the strong two-spin, DM, and KSEA interactions, the robustness of the produced two-spin non-localities can be improved.

DOI
10.1088/1402-4896/ac88ff

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Abstract This study explores the spontaneous emergence of local Fisher information and local quantum uncertainty beyond entanglement in a noisy two-qubit Heisenberg XXX model with Dzyaloshinskii-Moria (DM) and Kaplan-Shekhtman-Entin-Wohlman-Aharony (KSEA) interactions. Local quantum Fisher information, local quantum uncertainty, and logarithmic negativity are used to examine two-spin non-locality. We find that by employing strong two-spin, Dzyaloshinskii- Moriya, and Kaplan-Shekhtman-Entin-Wohlman-Aharony interactions, we can prevent noise-induced losses in local Fisher information, local quantum uncertainty, and logarithmic negativity. The robustness of the two-spin non-localities is greater for a strong spin’s coupling strength than for the strong DM and KSEA interactions. Local Fisher information and local quantum uncertainty, as well as logarithmic-negativity, display asymmetric behaviors with respect to two-spin coupling and symmetric behaviors with respect to the Dzyaloshinskii-Moriya and Kaplan-Shekhtman-Entin-Wohlman-Aharony interactions. At high bath temperatures, the phenomenon of sudden-death two-spin entanglement emerges. Furthermore, by combining the parameters of the strong two-spin, DM, and KSEA interactions, the robustness of the produced two-spin non-localities can be improved.
This study explores the dynamics of the formation of quantum correlations, namely: local quantum Fisher information and concurrence in a two-spin Heisenberg XXX system. The x-direction of Kaplan–Shekhtman–Entin–Wohlman–Aharony (KSEA) and Dzyaloshinskii–Moriya (DM) interactions as well as the intrinsic decoherence are considered. We show that the interactions are responsible of transforming separable states to correlated states. We point out that by strengthening the two-spin antiferromagnetic interaction coupling, it is possible to increase the capacity to develop semi-regularly maximal two-spin correlations. By increasing the DM and KSEA x-components, the two-spin XXX–Heisenberg exalts maximal local Fisher information and concurrence correlations with large amplitudes and high frequencies. As the intrinsic decoherence increases, the amplitudes and frequencies of the correlations decrease, which also causes the phenomena of sudden death–birth and sudden changes of the correlations. The two-spin correlation produced by the unitary x-component interactions can be shielded from the intrinsic decoherence by increasing the two-spin antiferromagnetic interaction coupling.
Abstract This paper investigates the dynamics of two-spin nonlocality generation in a Heisenberg XXX chain with Dzyaloshinskii-Moriya (DM) and Kaplan-Shekhtman-Entin-Wohlman-Aharony (KSEA) interactions. We analyze the two-spin nonlocality dynamics by using uncertainty-induced nonlocal-ity, maximal Bell inequality, and log-negativity. We demonstrate that a separable two-spin Heisen-berg XXX chain state, induced by two-spin antiferromagnetic interaction as well as x-component of DM and KSEA interactions, could evolve to maximal two-spin nonlocality state. The ability of preserving the maximal uncertainty-induced nonlocality can be enhanced by increasing the coupling strength of the spin-spin interaction coupling. The hierarchy principle is maintained for the two-spin Bell nonlocality and log-negativity entanglement. The two-spin log-negativity dynamics exhibits the phenomenon of sudden death and birth as a result of the intrinsic decoherence, which also causes a reduction in the two-spin nonlocalities. The two-spin uncertainty-induced nonlocality is more robust , against the intrinsic decoherence, than the other types of the nonlocality. The results indicate that by boosting the two-spin antiferromagnetic interaction, the produced nonlocalities (resulting from the DM and KSEA x-component interactions) can be shielded from the intrinsic decoherence effect.
This paper explores thermal quantum memory-assisted entropic uncertainty, Bell-non-locality, and entanglement in a two-qubit Heisenberg XXX chain with x-directional Dzyaloshinskii-Moriya (DM) and Kaplan-Shekhtman-Entin-Wohlman-Aharony (KSEA) interactions in thermal equilibrium. We find this crucial that the initial degree of nonlocality and entanglement in the two-qubit state entirely depends upon the temperature, orientation, and strength of the DM and KSEA interaction of the magnetic field. Among many other situations, the magnetic field characterized by DM interaction with minimal temperature, exchange coupling strength, and KSEA interaction is the most reliable for generating and maintaining maximal nonlocality and entanglement while completely suppressing entropic uncertainty. On the other hand, repeated revivals and non-Markovian dynamics have been observed when the magnetic field is characterized by exchange coupling constant, DM and KSEA interaction with a higher temperature limit. Except for temperature-based magnetic fields, we show that maximal entanglement and nonlocality are generated and preserved in the two qubits with zero-order entropic uncertainty, which we believe is a better result than previous studies.
In this paper, a two-spin-1/2 particle coupled via dipolar interaction with the interplay of antisymmetric Dzyaloshinskii–Moriya and symmetric Kaplan–Shekhtman–Entin–Wohlman–Aharony interactions is considered at thermal equilibrium. The local quantum uncertainty and local quantum Fisher information are investigated as the pairwise nonclassical correlations quantifiers. The effects of the different system parameters on the quantified quantum correlation are analyzed in detail. Our results showed that the two studied thermal quantum correlation measures have similar qualitative behavior as well as quantitative sometimes. Also, it is shown that the quantumness of correlations is lost as the temperature rises sufficiently. Nevertheless, the antisymmetric and symmetric contributions of spin-orbit coupling considerably improve the amount of quantum correlations. Our analysis emphasized also that the local quantum uncertainty is bounded by local quantum Fisher information.
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 In this study, the quantum-memory assisted entropic uncertainty (QM-EU) and entanglement dynamics of the two-qubit Heisenberg XXX chain have been explored in the presence of intrinsic decoherence. The effect of the x-component of Dzyaloshinskii-Moriya (DM) and Kaplan-Shekhtman-Entin-Wohlman-Aharony (KSEA) interactions has been considered. The generation and preservation of quantum memory and entanglement have been examined for various values of the DM, KSEA, spin-spin, and spin coupling strengths. The uncertainty negatively affects the entanglement and both have anti-correlation. The absence and presence of intrinsic decoherence prevail in differing impacts on the dynamics of the system. In the first case, prolonged entanglement preservation, uncertainty suppression, and oscillatory dynamics have been observed. Moreover, in order to achieve the best-prolonged entanglement preservation and relative reduction of the entropic uncertainty, we have analyzed several parameter settings. We find that the effects of raising the DM, KSEA, and spin-spin interaction individually and simultaneously are different. The individual and simultaneous increase of the DM, KSEA, and spin-spin interaction parameters control the degree of entanglement, entropic uncertainty, and primarily the dynamics of the system.