# Coherence manipulation with dephasing-covariant operations

## TL;DR

This paper characterizes the capabilities of dephasing-covariant quantum operations, showing their limitations and advantages in manipulating quantum coherence, with implications for resource theories and quantum information processing.

## Contribution

It introduces and analyzes dephasing-covariant operations and a state-specific class, revealing their operational power and limitations in coherence transformations.

## Key findings

- Pure-state transformations under DIO follow majorization.
- $
ho$-DIO can distill more coherence than DIO.
- In asymptotic limits, both sets achieve the same rates.

## Abstract

We characterize the operational capabilities of quantum channels which can neither create nor detect quantum coherence vis-\`a-vis efficiently manipulating coherence as a resource. We study the class of dephasing-covariant operations (DIO), unable to detect the coherence of any input state, as well as introduce an operationally-motivated class of channels $\rho$-DIO which is tailored to a specific input state. We first show that pure-state transformations under DIO are completely governed by majorization, establishing necessary and sufficient conditions for such transformations and adding to the list of operational paradigms where majorization plays a central role. We then show that $\rho$-DIO are strictly more powerful: although they cannot detect the coherence of the input state $\rho$, the operations $\rho$-DIO can distill more coherence than DIO. However, the advantage disappears in the task of coherence dilution as well as generally in the asymptotic limit, where both sets of operations achieve the same rates in all transformations.