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The Gram matrix of a set of quantum pure states plays key roles in quantuminformation theory. It has been highlighted that the Gram matrix of apure-state ensemble can be viewed as a quantum state, and the quantumness of apure-state ensemble can thus be quantified by the coherence of the Gram matrix[Europhys. Lett. \textbf{134} 30003]. Instead of the $l_1$-norm of coherenceand the relative entropy of coherence, we utilize the generalized$\alpha$-$z$-relative R\'enyi entropy of coherence of the Gram matrix toquantify the quantumness of a pure-state ensemble and explore its properties.We show the usefulness of this quantifier by calculating the quantumness of siximportant pure-state ensembles. Furthermore, we compare our quantumness withother existing ones and show their features as well as orderings.

Quantumness of pure-state ensembles via coherence of Gram matrix based on generalized $\alpha$-$z$-relative R\'enyi entropy