Kirkwood–Dirac quasiprobabilities for measurements related to mutually unbiased equiangular tight frames

Protocols of quantum information science often realize in terms of specially selected states. In particular, such states are used to perform measurements at the final stage of a protocol. This study aims to explore measurements assigned to a mutually unbiased-equiangular tight frame. The utilized method deals with Kirkwood–Dirac quasiprobabilities, which are increasingly used in contemporary research. These quasiprobabilities constitute a matrix that can be linked to unravelings of certain quantum channels. Using states of the given frame to build principal Kraus operators leads to quasiprobabilities that represent the measured state. The structure of a mutually unbiased-equiangular tight frame allows one to characterize entropies associated with a particular unraveling. To do this, we estimate some of the Schatten and Ky Fan norms of the matrix consisted of quasiprobabilities. New uncertainty relations in terms of Rényi and Tsallis entropies follow from the obtained inequalities. A utility of the presented inequalities is exemplified with mutually unbiased bases of a qubit and equiangular tight frames of a ququart.