Universal method to estimate quantum coherence

Abstract

Coherence is a defining property of quantum theory that accounts for quantum advantage in many quantum information tasks. Although many coherence quantifiers were introduced in various contexts, the lack of efficient methods to estimate them restricts their applications. In this paper, we tackle this problem by proposing one universal method to provide measurable bounds for most current coherence quantifiers. Our method is motivated by the observation that the distance between the state of interest and its diagonal parts in the reference basis, which lies at the heart of the coherence quantifications, can be readily estimated by the disturbance effect and uncertainty of the reference measurement. Thus, our method of bounding coherence provides a feasible and broadly applicable avenue for detecting coherence, facilitating its further practical applications.