Fractional time dynamics of quantum correlations and coherence in an interacting qubit-qutrit system

Abstract

Abstract This research explores the progression of fractional time dynamics of quantum entanglement, nonclassical correlations, and quantum coherence <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msub> <mml:mrow> <mml:mi>C</mml:mi> </mml:mrow> <mml:mrow> <mml:msub> <mml:mrow> <mml:mi>l</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>1</mml:mn> </mml:mrow> </mml:msub> </mml:mrow> </mml:msub> </mml:math> in a qubit-qutrit XXZ system through an in-depth analysis of the effects of the fractional parameter τ , the exchange interaction J , the XXZ exchange anisotropy δ , and the Dzyaloshinskii-Moriya interaction (DMI) D z , and the initial state. The results reveal that lower values of τ lead to a rapid and stable increase in quantum correlations (measured by logarithmic negativity, LN, and local quantum uncertainty (LQU) but cause a faster decay in coherence <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msub> <mml:mrow> <mml:mi>C</mml:mi> </mml:mrow> <mml:mrow> <mml:msub> <mml:mrow> <mml:mi>l</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>1</mml:mn> </mml:mrow> </mml:msub> </mml:mrow> </mml:msub> </mml:math> , indicating a quick loss of quantum superposition. Conversely, higher values of τ slow the dynamics of correlations, allowing coherence to persist longer. The exchange strength J similarly influences stability: low J values promote fast correlation formation but reduce coherence stability, while high J values stabilize coherence at the expense of slower correlation growth. As for the XXZ anisotropy δ and DMI strength D z , lower values promote rapid quantum correlation development but compromise coherence. In contrast, higher values help sustain <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msub> <mml:mrow> <mml:mi>C</mml:mi> </mml:mrow> <mml:mrow> <mml:msub> <mml:mrow> <mml:mi>l</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>1</mml:mn> </mml:mrow> </mml:msub> </mml:mrow> </mml:msub> </mml:math> over time, limiting the intensity of correlations. The initial state is also critical: an initially partially entangled state is more resilient to perturbations. It preserves correlations over time compared to a separable state, which exhibits cycles of entanglement creation and destruction. Thus, by tuning system parameters, it is possible to control the stability and duration of correlations and coherence, providing a framework for optimizing quantum systems in applications that require both strong entanglement and durable coherence, such as quantum computing and secure communication.