Joint Realizability Tradeoffs Bounded by Quantum Channel Incompatibility

Abstract

Incompatible quantum channels cannot be jointly and exactly realized, meaning that any approximate joint realization inevitably entails a tradeoff in implementation accuracy. While this notion of channel incompatibility unifies fundamental limitations such as measurement uncertainty, the no information without disturbance principle, and the no-cloning and no-broadcasting theorems, connecting these traditional relations directly to the resource-theoretic strength of incompatibility has remained elusive. In this Letter, we show that generalized robustness, a typical resource quantifier of channel incompatibility, lower bounds the total error of any approximate joint realization. Applying this result to measurement channels provides a unified, model-independent framework encompassing error-error and information-error-disturbance tradeoffs. Furthermore, our robustness-based evaluation of disturbance outperforms an algebraic bound for all POVMs in dimensions up to six.