Relative quantum coherence, incompatibility, and quantum correlations of states

TL;DR

This paper introduces the concept of relative quantum coherence between states, establishing its quantitative links with incompatibility and various quantum correlations, thereby unifying fundamental quantum features.

Contribution

It defines relative quantum coherence and demonstrates its connections to incompatibility and multiple quantum correlation measures, providing a unified framework.

Findings

Relative quantum coherence quantifies coherence of one state in the basis of another.

Connections established between relative coherence and quantum discord, entanglement, and other correlations.

The framework offers new insights into the intrinsic links among quantum features.

Abstract

Quantum coherence, incompatibility, and quantum correlations are fundamental features of quantum physics. A unified view of those features is crucial for revealing quantitatively their intrinsic connections. We define the relative quantum coherence of two states as the coherence of one state in the reference basis spanned by the eigenvectors of another one and establish its quantitative connections with the extent of mutual incompatibility of two states. We also show that the proposed relative quantum coherence, which can take any form of measures such as $l_1$ norm and relative entropy, can be interpreted as or connected to various quantum correlations such as quantum discord, symmetric discord, entanglement of formation, and quantum deficits. Our results reveal conceptual implications and basic connections of quantum coherence, mutual incompatibility, and quantum correlations.