Relating CP divisibility of dynamical maps with compatibility of channels

TL;DR

This paper explores the relationship between CP-divisibility and channel compatibility, showing that incompatibility robustness generally decreases in CP-divisible maps but can behave non-monotonically in CP-indivisible regimes, and proposes a new measure of CP-indivisibility.

Contribution

It establishes a link between CP-divisibility and channel incompatibility robustness, introducing a new measure for CP-indivisibility based on incompatibility robustness.

Findings

Incompatibility robustness is non-increasing in CP-divisible maps.

Non-monotonic behavior of incompatibility robustness observed in CP-indivisible maps.

Proposed a new measure of CP-indivisibility using incompatibility robustness.

Abstract

The role of CP-indivisibility and incompatibility as valuable resources for various information-theoretic tasks is widely acknowledged. This study delves into the intricate relationship between CP-divisibility and channel compatibility. Our investigation focuses on the behaviour of incompatibility robustness of quantum channels for a pair of generic dynamical maps. We show that the incompatibility robustness of channels is monotonically non-increasing for a pair of generic CP-divisible dynamical maps. Further, our explicit study of the behaviour of incompatibility robustness with time for some specific dynamical maps reveals non-monotonic behaviour in the CP-indivisible regime. Additionally, we propose a measure of CP-indivisibility based on the incompatibility robustness of quantum channels. Our investigation provides valuable insights into the nature of quantum dynamical maps and their relevance in information-theoretic applications.