Incompatibility of quantum channels

TL;DR

This paper characterizes when two quantum channels are compatible, showing that most noisy channels are compatible and linking incompatibility to fundamental quantum phenomena like measurement disturbance.

Contribution

It provides a new characterization of quantum channel compatibility using concatenation and conjugation, unifying various quantum features.

Findings

Most sufficiently noisy channels are compatible

Incompatibility relates to fundamental quantum phenomena

Framework unifies phenomena like broadcasting impossibility and measurement disturbance

Abstract

Two quantum channels are called compatible if they can be obtained as marginals from a single broadcasting channel; otherwise they are incompatible. We derive a characterization of the compatibility relation in terms of concatenation and conjugation, and we show that all pairs of sufficiently noisy quantum channels are compatible. The complement relation of incompatibility can be seen as a unifying aspect for many quantum features. We demonstrate that several phenomena, such as impossibility of universal broadcasting and unavoidable measurement disturbance, appear naturally in this framework.