Estimating quantum coherence using limited quantum resources

doi:10.1088/1674-1056/adfb56

Abstract Quantum coherence, as one of the most fundamental non-classical features in quantum mechanics, plays a pivotal role in various quantum information processing tasks, including quantum computing and quantum metrology. The robustness of quantum coherence (RoC) offers an operational interpretation by quantifying the advantage provided by a quantum state in phase discrimination tasks. To achieve verification RoC with high precision via semidefinite programming (SDP), complete knowledge of quantum states is typically required. Relying solely on expectation values of observables may introduce significant errors in SDP-based estimations. To estimate RoC with high precision using limited data extracted from quantum states, firstly, we propose a semi-supervised K-nearest neighbor (KNN) algorithm (semi-KNN) and a semisupervised method that combines the KNN and random forest (RF) models with a dynamical threshold (semi-KNN-RF). Then we implement the semi-KNN and semi-KNN-RF models to efficiently estimate quantum coherence by analyzing statistical data obtained from randomly generated local projective measurements performed on unknown quantum states. The semi-KNN-RF model performs better than the semi-KNN model. This innovative methodology allows for accurate coherence estimation, even for high-dimensional quantum systems.

Keywords: robustness of quantum coherence semi-K-nearest neighbors model semi-K-nearest neighbors and random forest model

Received: 28 May 2025
Revised: 23 July 2025
Accepted manuscript online: 14 August 2025

PACS:	03.65.Aa	(Quantum systems with finite Hilbert space)
	03.67.-a	(Quantum information)
	03.65.Ta	(Foundations of quantum mechanics; measurement theory)
	03.65.-w	(Quantum mechanics)

Fund: This work is supported by the National Natural Science Foundation of China (Grant No. 12071179).

Corresponding Authors: Zhihua Chen
E-mail: chenzhihua77@sina.com

Cite this article:

Bin Zou(邹斌), Kai Wu(吴凯), and Zhihua Chen(陈芝花) Estimating quantum coherence using limited quantum resources 2026 Chin. Phys. B 35 030301

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