We establish a lower bound on the quantum coherence of an arbitrary quantum state in arbitrary dimension, using a noncommutativity estimator of an arbitrary observable of sub-unit norm, where the estimator is the commutator of the observable and its incoherent or classical part. The relation provides a direct method of obtaining an estimate of the quantum coherence of an arbitrary quantum state, without resorting to quantum state tomography or the existing witness operators.
@article{arxiv.2004.07729,
title = {Estimating quantum coherence by noncommutativity of any observable and its incoherent part},
author = {Tanaya Ray and Ahana Ghoshal and Arun Kumar Pati and Ujjwal Sen},
journal= {arXiv preprint arXiv:2004.07729},
year = {2022}
}