Quantum coherence via conditional entropy

TL;DR

This paper develops a unified framework linking quantum coherence measures to general conditional entropies, revealing their operational meaning and relation to bipartite quantum correlations.

Contribution

It introduces a unified approach to redefine quantum coherence measures using general conditional entropies, extending previous relations based solely on Von-Neumann entropy.

Findings

Unified framework for coherence measures via conditional entropies

Numerical calculation of coherence measures using semi-definite programming

Highlights the link between single-party coherence and bipartite quantum correlations

Abstract

Quantum coherence characterizes the non-classical feature of a single party system with respect to a local basis. Based on a recently introduced resource framework, coherence can be regarded as a resource and be systematically manipulated and quantified. Operationally, considering the projective measurement of the state in the computational basis, coherence quantifies the intrinsic randomness of the measurement outcome conditioned on all the other quantum systems. However, such a relation is only proven when randomness is characterized by the Von-Neumann entropy. In this work, we consider several recently proposed coherence measures and relate them to the general uncertainties of the projective measurement outcome conditioned on all the other systems. Our work thus provides a unified framework for redefining several coherence measures via general conditional entropies. Based on the relation, we numerically calculate the coherence measures via semi-definite programming. Furthermore, we discuss the operational meaning of the unified definition. Our result highlights the close relation between single partite coherence and bipartite quantum correlation.