Scalable protocol to coherence estimation from scarce data: Theory and experiment

TL;DR

This paper introduces a scalable, efficient protocol for estimating quantum coherence from limited data, overcoming computational challenges and enabling analysis of large quantum systems.

Contribution

It proposes a novel relaxation of the coherence estimation problem into a computationally efficient optimization, scalable to large systems.

Findings

Protocol is experimentally demonstrated to be practical.

Computational cost is insensitive to system size.

Enables coherence estimation in data-scarce, large-scale quantum systems.

Abstract

Key quantum features like coherence are the fundamental resources enabling quantum advantages and ascertaining their presence in quantum systems is crucial for developing quantum technologies. This task, however, faces severe challenges in the noisy intermediate-scale quantum era. On one hand, experimental data are typically scarce, rendering full state reconstruction infeasible. On the other hand, these features are usually quantified by highly nonlinear functionals that elude efficient estimations via existing methods. In this work, we propose a scalable protocol for estimating coherence from scarce data and further experimentally demonstrate its practical utility. The key innovation here is to relax the potentially NP-hard coherence estimation problem into a computationally efficient optimization. This renders the computational cost in our protocol insensitive to the system size, in sharp contrast to the exponential growth in traditional methods. This work opens a novel route toward estimating coherence of large-scale quantum systems under data-scarce conditions.