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Physica Scripta

Dynamics of quantum-memory assisted entropic uncertainty of a two-spin Heisenberg XXX model under the intrinsic decoherence effect

A-B A Mohamed, Atta Ur Rahman, F. M. Aldosari, Hichem Eleuch

Published May 9, 2023• 7 citations

Abstract

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.

DOI: 10.1088/1402-4896/acced9

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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.

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.

Abstract In this paper, we have investigated the dynamical features of tripartite quantum-memory-assisted entropic uncertainty (tQMA-EU) and its two corresponding lower bounds in three-qubit Heisenberg XXZ spin chain model with Dzyaloshinskii-Moriya (DM) interaction and Kaplan-Shekhtman-Entin-Wohlman-Aharony (KSEA) interaction. The results show that, when the DM and KSEA interaction are taken account, the Dolatkhah's lower bound is always equal to the tQMA-EU and remains higher than the Ming's lower bound in both ferromagnetic and antiferromagnetic cases.The increasing of DM and KASE interactions can effectively reduce the value of tQMA-EU, the varying behaviors of tQMA-EU with respect to DM and KASE interactions from positive and negative intervals demonstrate central symmetry. Particularly, in ferromagnetic case, this reduction effect is more pronounced than that in antiferromagnetic case. In addition, the dynamical features of Dolatkhah's lower bound and Ming's lower bound with respect to the spin chain systemic parameters display distinct differences in the ferromagnetic and antiferromagnetic cases. Specifically, in the ferromagnetic case and with weak DM interaction, during the lower temperature range, under the influence of the KSEA interaction and under an external magnetic field, the Dolatkhah's lower bound dosen't negative-correlated to tripartite negativity quantum correlation N ABC . in contrast, the dynamics of Ming's lower bound show negative-correlated to N ABC .

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 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.

In this paper, the thermal quantum correlations along with the thermal entropic uncertainty in a two neighboring XYZ Heisenberg spin-1/2 particles subjected to a transverse external magnetic field with the interplay of both antisymmetric Dzyaloshinskii–Moriya and symmetric Kaplan–Shekhtman–Entin–Wohlman–Aharony are investigated. The quantum consonance and uncertainty-induced quantum nonlocality as well as the entropic uncertainty with quantum memory for the considered system are specified and the thermal behaviors of them in terms of the system parameters are examined. The expected decrease of quantum correlations for higher absolute temperatures is confirmed while the inflation of the uncertainty is generated. Moreover, we show that the stronger spin-spin and spin-orbit exchange couplings can enhance the thermal quantum correlations and suppress the uncertainty. Accordingly, our remarks are expected to be beneficent in illustrating the dynamical quantum correlations and entropy-based uncertainty in a general Heisenberg spin-chain model and thus would be useful for practical quantum information processing.

Abstract The precision of measurements for two incompatible observables in a physical system can be improved with the assistance of quantum memory. In this paper, we investigate the quantum-memory-assisted entropic uncertainty relation for a spin-1 Heisenberg model in the presence of external magnetic fields, the systemic quantum entanglement (characterized by the negativity) is analyzed as contrast. Our results show that for the XY spin chain in thermal equilibrium, the entropic uncertainty can be reduced by reinforcing the coupling between the two particles or decreasing the temperature of the environment. At zero-temperature, the strong magnetic field can result in the growth of the entropic uncertainty. Moreover, in the Ising case, the variation trends of the uncertainty are relied on the choices of anisotropic parameters. Taking the influence of intrinsic decoherence into account, we find that the strong coupling accelerates the inflation of the uncertainty over time, whereas the high magnetic field contributes to its reduction during the temporal evolution. Furthermore, we also verify that the evolution behavior of the entropic uncertainty is roughly anti-correlated with that of the entanglement in the whole dynamical process. Our results could offer new insights into quantum precision measurement for the high spin solid-state systems.