Estimating quantum coherence by noncommutativity of any observable and its incoherent part

Abstract

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.

arXiv commentv3: 5 pages, no figures

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Cited by in corpus (4)

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• Witnessing quantum coherence with prior knowledge of observables
• Scalable protocol to coherence estimation from scarce data: Theory and experiment
• Classifying coherence with a finite set of witnesses