Various versions of "independence" are actively inverstigated in quantum probability. In the context of relativistic QFT, we show here that the physical origin of "independence" can be sought in the asymptotic condition through which asymptotic fields and states exhibiting the independence emerge from the non-independent interacting Heisenberg fields in a kind of "central limit". From the algebraic viewpoint, this condition is equivalent to the on-shell condition to pick up free one-particle modes, which also reduces to Einstein's famous formula
E=mc2. A scenario to reconstruct interacting Heisenberg fields as Micro-objects from these "independent" =free Macro-objects intertwined by an S-matrix as a measurable quantity is formulated according to the Micro-Macro Duality associated with a new notion of a \textit{cocycle of K-T operators}.
Micro-Macro Duality means here the universal mutual relations between the microscopic quantum world and various macroscopic classical levels, which can be formulated mathematically as categorical adjunctions. It underlies a unified scheme for generalized sectors based upon selection criteria proposed by myself in 2003 to control different branches of physics from a unified viewpoint, which has played essential roles in extending the Doplicher-Haag-Roberts superselection theory to various situations with spontaneously as well as explicitly broken symmetries. Along this line of thought, the state correlations between a system and a measuring apparatus necessary for measurements can canonically be formulated within the context of group duality; the obtained measurement scheme is not restricted to the quantum mechanical situations with finite number of particles but can safely be applied to quantum field theory with infinite degrees of freedom whose local subalgebras are given by type III von Neumann algebras.