Perturbative distinguishability of black hole microstates from AdS/CFT correspondence

Abstract

We establish direct evidence for the perturbative distinguishability between black hole microstates and thermal states using the AdS/CFT correspondence. In two-dimensional holographic conformal field theories, we obtain the subsystem fidelity and quantum Jensen-Shannon divergence, both of which provide rigorous lower and upper bounds for subsystem trace distance. This result demonstrates that perturbative quantum gravity corrections break semiclassical indistinguishability, thereby supporting the recovery of information even from a small amount of the Hawking radiation.