Reversibility and Measurements

Abstract

This chapter is concerned with the approximate reversibility (sufficiency) for a sequence of quantum operations α _k : M _k → M (or quantum channels with input M and outputs M _k). Our main problem is to characterize the approximate reversibility of $(\alpha _k:M_k\to M)_{k=1}^\infty$ for $\psi ,\varphi \in M_*^+$ in terms of the convergence S _f(ψ ∘ α _k∥φ ∘ α _k) → S _f(ψ∥φ). In particular, we are concerned with the case where α _k’s are measurement operations with commutative M _k’s (or quantum-classical channels).