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Characterizing quantum ensemble using geometric measure of quantum coherence

The characterization of the quantum ensemble is a fundamental issue in quantum information theory and foundations. The ensemble is also useful for various quantum information processing. To characterize the quantum ensemble, in this article, we generalize the coherence measure of a state to the quantum ensemble. Exploiting the fidelity and affinity between the ensemble, we propose a quantumness quantifier for the quantum ensemble. It is shown that the proposed quantifier satisfies the necessary axioms of a bonafide measure of quantumness. Finally, we compute the quantumness of a few well-known ensembles.