Entropic Uncertainty for Two Coupled Dipole Spins Using Quantum Memory under the Dzyaloshinskii-Moriya Interaction

Ahmad N Khedr; Abdel-Baset A Mohamed; Abdel-Haleem Abdel-Aty; Mahmoud Tammam; Mahmoud Abdel-Aty; Hichem Eleuch

doi:10.3390/e23121595

Entropic Uncertainty for Two Coupled Dipole Spins Using Quantum Memory under the Dzyaloshinskii-Moriya Interaction

Entropy (Basel). 2021 Nov 28;23(12):1595. doi: 10.3390/e23121595.

Authors

Ahmad N Khedr¹, Abdel-Baset A Mohamed^{2

3}, Abdel-Haleem Abdel-Aty^{1

4}, Mahmoud Tammam¹, Mahmoud Abdel-Aty⁵, Hichem Eleuch^{6

7

8}

Affiliations

¹ Department of Physics, Faculty of Science, Al-Azhar University, Assiut 71524, Egypt.
² Department of Mathematics, College of Science and Humanities in Al-Aflaj, Prince Sattam bin Abdulaziz University, Al-Aflaj 11942, Saudi Arabia.
³ Department of Mathematics, Faculty of Science, Assiut University, Assiut 71515, Egypt.
⁴ Department of Physics, College of Sciences, University of Bisha, Bisha 61922, Saudi Arabia.
⁵ Department of Mathematics, Faculty of Science, Sohag University, Sohag 82524, Egypt.
⁶ Department of Applied Physics and Astronomy, University of Sharjah, Sharjah 27272, United Arab Emirates.
⁷ Department of Applied Sciences and Mathematics, College of Arts and Sciences, Abu Dhabi University, Abu Dhabi 59911, United Arab Emirates.
⁸ Institute for Quantum Science and Engineering, Texas A&M University, College Station, TX 77843, USA.

Abstract

In the thermodynamic equilibrium of dipolar-coupled spin systems under the influence of a Dzyaloshinskii-Moriya (D-M) interaction along the z-axis, the current study explores the quantum-memory-assisted entropic uncertainty relation (QMA-EUR), entropy mixedness and the concurrence two-spin entanglement. Quantum entanglement is reduced at increased temperature values, but inflation uncertainty and mixedness are enhanced. The considered quantum effects are stabilized to their stationary values at high temperatures. The two-spin entanglement is entirely repressed if the D-M interaction is disregarded, and the entropic uncertainty and entropy mixedness reach their maximum values for equal coupling rates. Rather than the concurrence, the entropy mixedness can be a proper indicator of the nature of the entropic uncertainty. The effect of model parameters (D-M coupling and dipole-dipole spin) on the quantum dynamic effects in thermal environment temperature is explored. The results reveal that the model parameters cause significant variations in the predicted QMA-EUR.

Keywords: Dzyaloshinskii–Moriya interaction; dipolar system; entanglement; mixedness; quantum-memory-assisted entropic uncertainty.