Ding Qi-Ming, Fang Xiao-Xu, Lu He
School of Physics, Shandong University, Jinan 250100, China.
Entropy (Basel). 2021 Nov 15;23(11):1519. doi: 10.3390/e23111519.
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, the l1-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. We observe that the spectrum-estimation-based method outperforms other methods in various coherence measures, which significantly enhances the accuracy of estimation.
检测多体量子相干性通常需要量子态重构，而这对于大规模量子系统而言效率相当低下。沿着这一研究方向，人们已经提出了几种无需量子态重构就能检测多体量子相干性的有效方法，其中基于谱估计的方法适用于各种相干性度量。在此，我们首先将基于谱估计的方法推广到相干性的几何度量。然后，我们研究各种相干性度量（包括相干性的几何度量、相干性的(l1)范数、相干性的鲁棒性以及一些多量子比特GHZ态和线性簇态相干性的凸顶量化器）估计下限的紧致性。最后，我们展示了基于谱估计的方法以及另外两种有效方法。我们观察到，基于谱估计的方法在各种相干性度量方面优于其他方法，这显著提高了估计的准确性。
