Abstract
Josza's definition of fidelity for a pair of (mixed) quantum states is studied in the context of two types of operator algebras. The first setting is mainly algebraic in that it involves unital C^*-algebras A that possess a faithful trace functional τ. In this context, the role of quantum states (that is, density operators) in the classical quantum-mechanical framework is assumed by positive elements ρ∈ A for which τ(ρ)=1. The second of our two settings is more operator theoretic: by fixing a faithful normal semifinite trace τ on a semifinite von Neumann algebra M, we define and consider the fidelity of pairs of positive operators in M of unit trace. The main results of this paper address monotonicity and preservation of fidelity under the action of certain trace-preserving positive linear maps of A or of the predual M_*. Our results also yield a new proof of a theorem of Moln\'ar on the structure of quantum channels on the trace-class operators that preserve fidelity.