Quantifying dynamical coherence with coherence measures

TL;DR

This paper introduces a new way to quantify dynamical quantum coherence using coherence measures, overcoming previous challenges in defining incoherent operations without relying on incoherent states.

Contribution

It proposes an alternative definition of incoherent operations induced by coherence measures and applies it to quantify POVM-based dynamical coherence.

Findings

Introduced an alternative definition of incoherent operations.

Quantified POVM-based dynamical coherence.

Provided a framework for measuring dynamical coherence.

Abstract

Quantum coherence, like entanglement, is a fundamental resource in quantum information. In recent years, remarkable progress has been made in formulating resource theory of coherence from a broader perspective. The notions of block-coherence and POVM-based coherence have been established. Certain challenges, however, remain to be addressed. It is difficult to define incoherent operations directly, without requiring incoherent states, which proves a major obstacle in establishing the resource theory of dynamical coherence. In this paper, we overcome this limitation by introducing an alternate definition of incoherent operations, induced via coherence measures, and quantify dynamical coherence based on this definition. Finally, we apply our proposed definition to quantify POVM-based dynamical coherence.