Understanding two-dimensional electron gas (2DEG) systems is crucial for a comprehensive grasp of their quantum potential. Due to the spins of electrons, 2DEG systems present a scalable and practical platform for housing qubits in quantum information processing. This paper investigates how the distance between delocalized electrons and electron density influences the dynamic behavior of the quantum-memory-assisted entropic uncertainty relation ( \(\mathcal {QMA-EUR}\) ) and non-classical correlations in 2DEG systems. Geometric quantum metrics, such as Bures distance entanglement ( \(\mathcal {B}\) ), measure the entanglement between the spins of two delocalized electrons, while trace distance discord ( \(\mathcal {TDD}\) ) assesses quantum correlations in 2DEG systems. The results indicate that electron density in 2DEGs is crucial for preserving quantum correlations and reducing \(\mathcal {QMA-EUR}\) . Moreover, the findings suggest that electron separations have a detrimental effect on entanglement and non-classical correlations in these systems. It is demonstrated that \(\mathcal {QMA-EUR}\) behaves inversely to quantum correlations of electron spins in 2DEGs. Additionally, by adjusting electron density thoughtfully, quantum correlations can be strengthened against electron separation, ultimately reducing \(\mathcal {QMA-EUR}\) . These insights open up fascinating prospects for harnessing 2DEG systems in quantum information processing.
