Quantumness of Pure-State Ensembles via Coherence of Gram Matrix Based on Generalized α-z-Relative Renyi Entropy

The Gram matrix of a set of quantum pure states plays key roles in quantum information theory. It has been highlighted that the Gram matrix of a pure-state ensemble can be viewed as a quantum state, and the quantumness of a pure-state ensemble can thus be quantified by the coherence of the Gram matrix [Europhys. Lett. 134, 30003]. Instead of the l(1)-norm of coherence and the relative entropy of coherence, we utilize the generalized alpha-z-relative Renyi entropy of coherence of the Gram matrix to quantify the quantumness of a pure-state ensemble and explore its properties. We show the usefulness of this quantifier by calculating the quantumness of six important pure-state ensembles. Furthermore, we compare our quantumness with other existing ones and show their features as well as orderings.