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

Abstract In this study, we explore the dynamics of a hybrid quantum system composed of qubits and qutrits under fractional time evolution. The key parameters—fractional parameter τ, exchange interaction J, XXZ anisotropy δ, and Dzyaloshinskii-Moriya interaction (DMI) Dz—significantly impact quantum correlations and coherence. The fractional parameter τ controls the growth of quantum correlations and coherence stabilization: small values accelerate correlation formation but reduce coherence, while larger values allow slower correlation growth and preserve coherence. The exchange interaction J balances coherence and correlations, with higher values stabilizing coherence at the cost of entanglement, and lower values enhancing correlations but weakening coherence. The XXZ anisotropy δ modifies this balance, where higher values favor coherence and suppress correlations, and smaller values improve correlations but reduce coherence. Finally, the Dzyaloshinskii-Moriya interaction Dz provides fine-tuned control, stabilizing both coherence
 and correlations at higher values and potentially enhancing entanglement and negativity. This study offers a deeper understanding of the interplay between these parameters and their influence on hybrid qubit-qutrit systems, paving the way for advancements in quantum information and computing applications.