Stochastic linear maps and transition probability

Abstract

Some aspects of the transition probability P(ω, ν) between states ω, ν on unital *-algebras are discussed. It is shown that P increases under the action of any stochastic linear map T, i.e., P(Tω, Tν)⩾P(ω, ν). Some properties of P are derived in starting from a recently-proved characterization of the quantity in question.