# Deterministic Coherence Distillation

## TL;DR

This paper establishes the necessary and sufficient conditions for deterministic coherence distillation from mixed to pure states under strictly incoherent operations, linking resource theory and algebraic majorization, and provides a scheme for optimal distillation.

## Contribution

It introduces a complete characterization of deterministic coherence distillation under strictly incoherent operations, including a new distillation scheme and maximum achievable coherence.

## Key findings

- Derived necessary and sufficient conditions for state transformation.
- Connected coherence resource theory with majorization lattice.
- Proposed an optimal deterministic coherence distillation scheme.

## Abstract

Coherence distillation is one of the central problems in the resource theory of coherence. In this Letter, we complete the deterministic distillation of quantum coherence for a finite number of coherent states under strictly incoherent operations. Specifically, we find the necessary and sufficient condition for the transformation from a mixed coherent state into a pure state via strictly incoherent operations, which recovers a connection between the resource theory of coherence and the algebraic theory of majorization lattice. With the help of this condition, we present the deterministic coherence distillation scheme and derive the maximum number of maximally coherent states obtained via this scheme.