Geometric Quantum Resources and Linear Entropy in a Double Quantum Dot under Thermal and Magnetic Field Effects

We study bipartite entanglement, quantum coherence, and linear-entropy-based distance in a semiconductor double quantum dot (DQD) hosting a single electron, subject to longitudinal Zeeman splitting, a transverse magnetic field gradient, and thermal fluctuations. In this single-electron system, modeled as a two-qubit system, intrinsic correlations arise from the interplay between the charge-localization and spin degrees of freedom. Entanglement is quantified via the Bures distance, coherence through the Hellinger distance, and linear-entropy-based distance is used as a quantitative measure to characterize the purity of the corresponding quantum thermal state. Our results demonstrate how temperature T, the strength of applied magnetic fields, and the intrinsic DQD parameters shape the behavior of these quantum resources (QR), revealing that careful adjustment of the DQD parameters and the intensities of the two perpendicular external magnetic fields provides a practical handle for controlling the quantum properties of the system and preserving quantum resources against the detrimental effects of thermal noise. We further show that Hellinger coherence is more robust than entanglement against thermal noise, underscoring its potential as a reliable quantum resource in solid-state quantum information platforms.