Confinement as Information-Geometric Rigidity of Non-Markovian Quantum Channels: String Tension, Casimir Scaling, and a Geometric Order Parameter from ICC

This paper is part of the Information-Copying Cosmology (ICC) series. We propose a geo metric formulation of confinement in SU(3) gauge theory in terms of the information geometry of non-Markovian quantum channels. We work within the ICC framework, where spacetime and gauge fields emerge from a CPTP network with Bures geometry. We show that confinement is equivalent to the extensivity of conditional mutual information (CMI), which arises from a finite spectral gap of a CPTP vacuum channel. By endowing the manifold of Choi states with the Bures metric, we demonstrate that confinement corresponds to positive Ricci curvature, which enforces a non-vanishing bulk quantum Fisher information (QFI) density. We establish: (i) a no-go theorem excluding confinement in flat channel geometry, (ii) a rigidity theorem providing a strict lower bound on the string tension, and (iii) a universality theorem showing the RG invariance of Casimir scaling. Furthermore, Wilson loops are shown to correspond to the relative entropy of gauge defects, bounded by the optimal state reconstruction cost via the Petz recovery map. This framework unifies lattice QCD phenomenology, holographic reconstruction principles, and quantum information geometry into a single, rigorous theoretical structure