Entropic uncertainty and coherence in Einstein-Gauss-Bonnet gravity

Abstract: We investigate tripartite quantum-memory-assisted entropic uncertain and quantum coherence for GHZ and W states of a fermionic field in the background of a spherically symmetric black hole of Einstein-Gauss-Bonnet (EGB) gravity. Two distinct scenarios are analyzed: (i) the quantum memories (held by Bob and Charlie) are near the horizon while the measured particle (Alice) remains in the flat region, and (ii) the reverse configuration. Dimensional dependence is observed: in $d>5$ dimensions, the measurement uncertainty decreases monotonically with increasing horizon radius, while coherence increases; in $d=5$, both quantities exhibit non-monotonic behavior due to distinctive thermodynamic properties. Furthermore, comparative analysis reveals that the W state exhibits higher robustness in preserving coherence, whereas the GHZ state shows greater resistance to measurement uncertainty increase induced by Hawking radiation. Notably, the two scenarios yield qualitatively distinct behaviors: quantum coherence is consistently lower in Scenario 1 (quantum memory near horizon) than in Scenario 2 (measured particle near horizon), irrespective of the quantum state. For measurement uncertainty, the W state displays lower uncertainty in Scenario 1, while the GHZ state exhibits the opposite trend, with higher measurement uncertainty in Scenario 1. These results indicate that the characteristics of different quantum resources provide important insights into the selection and optimization of quantum states for information processing in curved spacetime.