Applications of Quantum Information: From Black Hole Geometries to Gaussian Error Channels

In this work, we develop theoretical tools to explore
quantum correlations within the AdS/CFT framework. We examine the
holographic realization of optimized correlation measures in two-dimensional
thermal states corresponding to spacetimes with black hole horizons, enhancing
our understanding of how geometry encodes entanglement in AdS/CFT. We
further introduce cutoff-independent regularization techniques to compute these
entropies - addressing divergences due to infinite volume near the AdS
boundary. In the next part, we apply quantum information theory in practical
scenarios, demonstrating that channel capacity does not always determine
performance in single-shot contexts and modeling entanglement swapping
experiments using Gaussian error channels.