Detecting coherence via spectrum estimation

TL;DR

This paper introduces an efficient, experiment-friendly method for quantifying quantum coherence and spectrum estimation using majorization theory, enabling practical analysis of coherence phenomena in quantum systems.

Contribution

It presents a novel approach based on majorization theory for measuring quantum coherence and spectrum estimation that is practical for experiments and applicable to various quantum information tasks.

Findings

Provides a method to prove the presence of coherence.

Offers a precise lower bound for coherence quantification.

Demonstrates characterization of coherence freezing with minimal measurements.

Abstract

Coherence is a basic phenomenon in quantum mechanics and considered to be an essential resource in quantum information processing. Although the quantification of coherence has attracted a lot of interest, the lack of efficient methods to measure the coherence in experiments limits the applications. We address this problem by introducing an experiment-friendly method for coherence and spectrum estimation. This method is based on the theory of majorization and can not only be used to prove the presence of coherence, but also result in a rather precise lower bound of the amount of coherence. As an illustration, we show how to characterize the freezing phenomenon of coherence with only two local measurements for any $N$-qubit quantum systems. Our approach also has other applications in quantum information processing, such as the characterization of distillability and entanglement transformations.