The tightness of multipartite coherence from spectrum estimation

TL;DR

This paper extends spectrum-estimation methods to quantify multipartite quantum coherence efficiently, demonstrating improved accuracy over existing methods on experimental data.

Contribution

It generalizes spectrum-estimation-based coherence measurement to geometric measures and analyzes the tightness of bounds for various coherence measures.

Findings

Spectrum-estimation-based method outperforms others in accuracy.

The method is applicable to multiqubit GHZ and linear cluster states.

Experimental data confirms the method's effectiveness.

Abstract

Detecting multipartite quantum coherence usually requires quantum state reconstruction, which is quite inefficient for large-scale quantum systems. Along this line of research, several efficient procedures have been proposed to detect multipartite quantum coherence without quantum state reconstruction, among which the spectrum-estimation-based method is suitable for various coherence measures. Here, we first generalize the spectrum-estimation-based method for the geometric measure of coherence. Then, we investigate the tightness of the estimated lower bound of various coherence measures, including the geometric measure of coherence, $l_1$-norm of coherence, the robustness of coherence, and some convex roof quantifiers of coherence multiqubit GHZ states and linear cluster states. Finally, we demonstrate the spectrum-estimation-based method as well as the other two efficient methods by using the same experimental data [Ding et al. Phys. Rev. Research 3, 023228 (2021)]. We observe that the spectrum-estimation-based method outperforms other methods in various coherence measures, which significantly enhances the accuracy of estimation.