OPTIMAL BOUNDS ON FUNCTIONS OF QUANTUM STATES UNDER QUANTUM CHANNELS

Abstract

Let rho(1), rho(2) be quantum states and (rho(1), rho(2)) bar right arrow D(rho(1), rho(2)) be a scalar function such as the trace distance, the fidelity, and the relative entropy, etc. We determine optimal bounds for D(rho(1), Phi(rho(2))) for Phi is an element of S for different class of functions D(., .), where S is the set of unitary quantum channels, the set of mixed unitary channels, the set of unital quantum channels, and the set of all quantum channels.