Minimum relative entropies of low-dimensional spin systems

Work of Band and Park in the mid-1970's in which they proposed — on information-theoretic grounds — an alternative to the von Neumann entropy measure, S(ϱ) = -Tr ϱ ln ϱ, of a density matrix (ϱ) has apparently not been further applied. In this paper, however, specific measures are generated of the information-theoretic entropy of spin-12, spin-1 and two-photon mixed states. For this purpose, the minimum relative entropies of arbitrary mixed states with respect to uniform prior distributions over the pure states are determined. Though Band and Park did not specifically discuss this approach, it is contended that it is harmonious with their position. The duality theory of convex programming is employed to interrelate the von Neumann entropy and the minimum relative entropy measure adopted. Some concluding remarks are made on the possible use of such relative entropy indices in modeling the nonunitary (irreversible) evolution of quantum systems.