Geometric methods in quantum information and entanglement variational principle
arXiv:2403.13102 · doi:10.1142/s0219887824400103
Abstract
Geometrical methods in quantum information are very promising for both providing technical tools and intuition into difficult control or optimization problems. Moreover, they are of fundamental importance in connecting pure geometrical theories, like GR, to quantum mechanics, like in the AdS/CFT correspondence. In this paper, we first make a survey of the most important settings in which geometrical methods have proven useful to quantum information theory. Then, we lay down a general framework for an action principle for quantum resources like entanglement, coherence, and anti-flatness. We discuss the case of a two-qubit system.
Slighted expanded version with respect to the article that appeared in the International Journal of Geometric Methods in Modern Physics (https://doi.org/10.1142/s0219887824400103)