Joint Realizability Tradeoffs Bounded by Quantum Channel Incompatibility

TL;DR

This paper establishes a fundamental link between quantum channel incompatibility and the limits of approximate joint realizations, using robustness as a key resource measure.

Contribution

It introduces a robustness-based framework that bounds the total error in approximate joint realizations of incompatible quantum channels.

Findings

Robustness lower bounds the total error in joint realizations.

The framework unifies various quantum tradeoff relations.

Disturbance evaluation using robustness outperforms algebraic bounds up to dimension six.

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.