Realization of Relative Entropy Evolution in the Sudarshan-Lindblad for two Quantum Systems

Abstract

The idea of this paper is to investigate and realizing the quantum relative entropy normally used in quantum information using physical systems for two quantum systems. We have described these respectively by Hamiltonian and Lindblad operators , and we calculate the rate at which the relative entropy distance between the states evolving according to their two systems evolve. A consequence of the Baker–Campbell–Haussdorff formula in lie algebra theory, the computation uses the differentiation formula for the exponential map. The asymptotic formula for this relative entropy rate is obtained in terms of the scattering matrix corresponding to the two Hamiltonian.