Uncertainty relations for quantum coherence with respect to mutually unbiased equiangular tight frames

Abstract

The role of quantum coherence as an information resource has attracted increasing attention in recent years. Many protocols of quantum information science deal with specially selected states. Complete sets of mutually unbiased bases and symmetric informationally complete measurements are widely used in this regard. Other constructions were found to be useful, including projective designs and equiangular tight frames. As a rule, there are additional restrictions on the probabilities generated by quantum measurements assigned to such sets. Inequalities in terms of coherence quantifiers allow one to examine complementarity with respect to different sets. This study aims to examine uncertainty relations for coherence quantifiers averaged with respect to a set of mutually unbiased bases equiangular tight frames. To quantify the amount of coherence, quantum coherence quantifiers of the Tsallis type and the geometric coherence are used. The first case is induced by the Tsallis relative entropies. The derived inequalities are exemplified with equiangular tight frames of a ququart.