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.

v3: 5 pages, no figures

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Cited by in corpus (4)

• Resource theory of quantum coherence with probabilistically non-distinguishable pointers and corresponding wave-particle duality
• 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