# Coherence of Purification

## TL;DR

The paper introduces the coherence of purification as a new measure of total quantumness in a quantum system, exploring its properties, relationships with other quantum measures, and its role as a resource in quantum information tasks.

## Contribution

It defines the coherence of purification, proves its properties, and demonstrates its significance in quantifying quantumness and resourcefulness in quantum information processing.

## Key findings

- Coherence of purification always exceeds the system's coherence.
- For pure states, it equals the relative entropy of coherence.
- It can capture residual quantumness after dephasing.

## Abstract

We introduce a quantity called the coherence of purification which can be a measure of total quantumness for a single system. We prove that coherence of purification is always more than the coherence of the system. For a pure state, the coherence of purification is same as the relative entropy of coherence. Furthermore, we show that the difference in the coherence of purification of a quantum state before and after the dephasing can capture residual quantumness. In addition, we show that the entanglement of purification that can be created by incoherent operation between two subsystems is upper bounded by the coherence of purification of the original system. We show that the coherence of purification is a resource in quantum state discrimination process. In the absence of coherence, entanglement and quantum correlations, the coherence of purification may play an important role in quantum information processing tasks.