Behavioral Health Research Center of the Southwest

Finite-Dimensional Modular Theory, Non-Commutative Relative-Entropy Geometry, and Resilient Quantum Mirror Descent for Holographic State Reconstruction (Version 3)

Abstract We establish an exact mathematical framework connecting finite-dimensional Tomita–Takesaki modular theory, Kubo–Mori–Bogoliubov (KMB) Riemannian geometry, and entropic optimization for quantum states. First, we prove that the second directional derivative (Hessian) of th...