Correlations in a quantum-gravitationally coupled masses

This study investigates the thermal and magnetic field dependencies of quantum coherence, quantum negativity, Local Quantum Uncertainty ([Formula: see text]), and Local Quantum Fisher Information ([Formula: see text]) in quantum-gravitationally coupled masses. Quantum negativity exhibits distinct peak behavior with shifts in temperature and decreases in magnitude as the magnetic field strength increases, highlighting the influence of stronger fields on the optimal temperature range, while quantum coherence displays a peak that shifts to higher temperatures, with its value decreasing due to thermal effects. The analysis reveals that thermal effects reduce coherence but moderate the suppression caused by the magnetic field, particularly at higher temperatures, in addition the dependence of quantum negativity on magnetic field strength, gravitational parameter, and coupling strength shows non-monotonic behavior with respect to the magnetic field and a monotonic increase with the gravitational parameter and stronger magnetic coupling suppresses quantum negativity. Moreover, [Formula: see text] and [Formula: see text] show significant dependence on temperature and energy gap due to the magnetic field strength, [Formula: see text] demonstrates a peak with broadening and reduced sensitivity to variations in the energy gap at higher temperatures, and shows a peak at low magnetic field strengths and decays as the field increases, with the decay more pronounced at lower temperatures while [Formula: see text] exhibits a more pronounced sensitivity to the energy gap at lower temperatures, with decreasing sensitivity as the temperature rises and exhibits a greater sensitivity to the magnetic field at lower temperatures, with a peak at a specific magnetic field and more gradual decay at higher temperatures.