Entanglement degradation as a tool to detect signatures of modified gravity

We investigate entanglement degradation in the vicinity of a quantum corrected black hole. We consider a biprtite system (Alice-Rob) with Alice freely falling (radially) into the event horizon of a quantum corrected black hole and Rob being in the vicinity of the event horizon of the black hole. We consider a maximally entangled state (in the Fock basis) and start with the basic assumption that Rob is an uniformly accelerated observer. We then give a pedagogical analysis of the relation involving the Minkowski vaccum state and Rindler number states. Following the analogy given in Martín-Martínez et al. [Phys. Rev. D 82, 064006 (2010)], we establish the relation between the Hartle-Hawking vacuum state and Boulware and anti-Bouware number states from the Minkowski-Rindler relation. We then write down the quantum corrected black hole metric by making use of the near horizon approximation in an appropriate form. Next, we obtain the analytical forms of logarithmic negativity and mutual information and plot as a function of Rob's distance from the $r=0$ point. We observe that the entanglement degradation slows down because of the structural change in the lapse function of the metric via the incorporation of quantum gravity corrections in the Schwarzschild black hole. It is crucial to understand that any modified gravity theories that changes the metric structure results in a different rate of degradation of the entanglement. At the horizon radius, the entanglement degradation is always complete irrespective of the underlying theory. This observation may lead to the identification of the signature of modified gravity theories in a future generation of advanced observational scenarios. Such a modification can come from higher curvature corrections, higher dimensional gravity theories, quantum gravity corrections, etc. We can also interpret this effect as a noisy quantum channel with an operator sum representation of a completely positive and trace preserving map. We then finally obtain the entanglement fidelity using this operator sum representation.