Evolution equation for quantum coherence

TL;DR

This paper derives an evolution equation for quantum coherence in states under fully and strictly incoherent operations, generalizing entanglement evolution equations and introducing new coherence measures.

Contribution

It introduces the G-coherence and convex roof of G-coherence, proving their properties, and generalizes the coherence evolution equation to arbitrary d-dimensional states.

Findings

G-coherence is a strong coherence monotone.

Convex roof of G-coherence is a coherence measure.

Derived a general coherence evolution equation for d-dimensional states.

Abstract

Quantum coherence plays an important role in quantum resource theory, which is strongly related with entanglement. Similar to the entanglement evolution equation, we find the coherence evolution equation of quantum states through fully and strictly incoherent operation (FSIO) channels. In order to quantify the full coherence of qudit states, we define G-coherence and convex roof of G-coherence, and prove that the G-coherence is a strong coherence monotone and the convex roof of G-coherence is a coherence measure under FSIO, respectively. Furthermore, we prove a coherence evolution equation for arbitrary $d$-dimensional quantum pure and mixed states under FSIO channels, which generalizes the entanglement evolution equation for bipartite pure states. Our results will play an important role in the simplification of dynamical coherence measure.